\documentclass[11pt,b4j,dvipdfmx,landscape,twocolumn,papersize]{jsarticle}
% furikana.sty	http://xymtex.com/fujitas2/texlatex/index.html#tategumi
\usepackage{ascmac,bm,amssymb}
\usepackage[deluxe]{otf}
\usepackage{graphicx,color}
%\usepackage{qrcode}
%\usepackage[pdfpagemode=FullScreen,setpagesize=false]{hyperref}
%\usepackage[pdfstartview={XYZ null null 1.75},setpagesize=false]{hyperref}
\usepackage{hyperref,pxjahyper}
\usepackage{tikz}
\usetikzlibrary{calc}
%\usetikzlibrary{intersections,patterns,angles,backgrounds,positioning}

%\AtBeginDvi{\special{pdf:pagesize width 364mm height 257mm}}
\textwidth=330truemm \textheight=226truemm \columnseprule=0pt
\topmargin=-24truemm \oddsidemargin=-8truemm

\hypersetup{% Oct 1 2023
	pdftitle={数学授業プリント},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/math_ia/math_ia.htm}
	}

\newenvironment{nidan}{\begin{minipage}[t]{.225\textwidth}}{\end{minipage}}
%\def\nidangumi#1#2{\begin{nidan}{#1}\end{nidan}\quad%
%\begin{nidan}{#2}\end{nidan}}
\newcommand{\nidangumi}[2]{\begin{nidan}{#1}\end{nidan}\quad%
\begin{nidan}{#2}\end{nidan}}

% ■■■ 0より大きいときはdvipdfmxで印刷用PDFを作ることを想定（答えはプリント
% 下部に出力される）
%        0 のときはdvipdfmxでデジタル教材用PDFを作ることを想定（答えは問題の
% すぐ横に赤で出力され、後でOneNoteで黒く塗りつぶし）
\def\make_pdf_with_insatsu{1}

\everymath{\displaystyle}
\parindent=0zw \columnsep=3zw
\lineskiplimit=1ex \normallineskiplimit=\lineskiplimit 
\lineskip=\lineskiplimit \normallineskip=\lineskiplimit

\newcounter{toi} \newcounter{subtoi}[toi]
\newcounter{subsubtoi}[subtoi]

\def\toi{\refstepcounter{toi}\par          % 問
  \makebox[2zw][r]{\Large\ajKaku{\value{toi}}\hspace{0.5zw}}%
  \hangindent=2zw}

\def\subtoi{\refstepcounter{subtoi}\par    % 小問
  \makebox[3.4zw][r]{\ajKakko{\value{subtoi}}\hspace{1zw}}%
  \hangindent=3.4zw}

\def\subsubtoi{\refstepcounter{subsubtoi}\par    % 小小問
  \makebox[4.2zw][r]{\ajMaru{\value{subtoi}}\hspace{1zw}}%
  \hangindent=4.2zw}

\ifnum\make_pdf_with_insatsu>0
	\def\kotae#1{\relax}
\else
	\def\kotae#1{\hfill \textcolor{red}{\footnotesize\gtfamily\bfseries\(\boldsymbol{#1} \)}}
\fi

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-0.2em／\hfil\crcr$#1$}}
\pagestyle{empty}

\makeatletter
\def\hooklen#1#2{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother


\begin{document}
%
%  ===========================以下本文===============================
%
\def\namae{%
{\Large\gtfamily\bfseries 数学I \quad 授業プリント \# 61}\hfill
年\hskip8ex 組\hskip8ex 号 \hskip5ex

\hfill 
\underline{氏名\rule[-2ex]{0cm}{6ex}\hskip30ex}}

\namae

\vskip-2ex

{\large\gtfamily\bfseries ■　復習}

{\gtfamily\bfseries （復習）}次の直角三角形を
用いて，\( 30^\circ,~45^\circ,~60^\circ,~120^\circ,~135^\circ,~150^\circ \) の
\( \sin ,~\cos , ~\tan \) の値を求めなさい。

\hspace*{15mm}
\begin{tikzpicture}[rotate=0, scale=1.2, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1.732,1);
\coordinate (B) at ($ ({sqrt(3)},1) $);% (1.732,1);
\coordinate (A) at (0,0);
\coordinate (C) at ($ ({sqrt(3)},0) $);% (1.732,0);
\draw (A)--(B)--(C)--cycle;
%\draw (1.532,0)--(1.532,0.2)--(1.732,0.2);
\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
%\draw[dashed] (A) to[out=-30,in=-150] node [solid, inner sep=2pt, fill=white]{\small $\sqrt{3}$} (C);
%\draw[dashed] (A) to[out=60,in=180] node [inner sep=2pt, fill=white]{\small $2$} (B);
%\draw[dashed] (C) to[out=45,in=-45] node [inner sep=2pt, fill=white]{\small $1$} (B);
\draw(8pt,0) arc [start angle=0, end angle=30,x radius=8pt, y radius=8pt];
\draw(10pt,0) arc [start angle=0, end angle=30,x radius=10pt, y radius=10pt];
\draw(20pt,5pt) node{\footnotesize $30^\circ$};
\draw(B) +(0,-5pt) arc [start angle=270, end angle=210,x radius=5pt, y radius=5pt];
\draw(B) +(-5pt,-10pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}
%
\hspace*{7zw}
%
\begin{tikzpicture}[rotate=0, scale=1.2, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1,1);
\coordinate (B) at (1,1);
\coordinate (A) at (0,0);
\coordinate (C) at (1,0);
\draw (A)--(B)--(C)--cycle;
%\draw (0.8,0)--(0.8,0.2)--(1,0.2);
\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
%\draw[dashed] (A) to[out=-45,in=-135] node [inner sep=2pt, fill=white]{\small $1$} (C);
%\draw[dashed] (A) to[out=90,in=180] node [solid, inner sep=1pt, fill=white]{\small $\sqrt{2}$} (B);
%\draw[dashed] (C) to[out=45,in=-45] node [inner sep=2pt, fill=white]{\small $1$} (B);
\draw(5pt,0) arc [start angle=0, end angle=45,x radius=5pt, y radius=5pt];
\draw(12pt,5pt) node{\footnotesize $45^\circ$};
\draw(B) +(0,-5pt) arc [start angle=270, end angle=225,x radius=5pt, y radius=5pt];
\draw(B) +(-5pt,-13pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}
%
\hspace*{7zw}
%
\begin{tikzpicture}[rotate=0, scale=1.2, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1,1.732);
\coordinate (B) at ($ (1,{sqrt(3)}) $);% (1,1.732);
\coordinate (A) at (0,0);
\coordinate (C) at (1,0);
\draw (A)--(B)--(C)--cycle;
%\draw (0.8,0)--(0.8,0.2)--(1,0.2);
\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
%\draw[dashed] (A) to[out=-45,in=-135] node [inner sep=2pt, fill=white]{\small $1$} (C);
%\draw[dashed] (A) to[out=90,in=210] node [inner sep=2pt, fill=white]{\small $2$} (B);
%\draw[dashed] (C) to[out=45,in=-45] node [inner sep=2pt, fill=white]{\small $\sqrt{3}$} (B);
\draw(5pt,0) arc [start angle=0, end angle=60,x radius=5pt, y radius=5pt];
\draw(12pt,5pt) node{\footnotesize $60^\circ$};
\draw(B) +(0,-8pt) arc [start angle=270, end angle=240,x radius=8pt, y radius=8pt];
\draw(B) +(0,-10pt) arc [start angle=270, end angle=240,x radius=10pt, y radius=10pt];
\draw(B) +(-5pt,-20pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}

\bigskip

%\def\sikaku{\raisebox{0mm}{\fbox{\rule[-5mm]{0mm}{12mm}\hskip 10 mm}}}
\def\sikaku{\raisebox{0mm}{\fbox{\rule[-4mm]{0mm}{10mm}\hskip 8mm}}}
\def\naraberu#1{\( \makebox[7ex][l]{\(#1 30^\circ\)}= \) \sikaku\hfill
	\( \makebox[7ex][l]{\(#1 45^\circ\)} = \) \sikaku\hfill
	\( \makebox[7ex][l]{\(#1 60^\circ\)} =\) \sikaku\hfill}

\hfill\naraberu{\sin}\mbox{}

\hfill\naraberu{\cos}\mbox{}

\hfill\naraberu{\tan}\mbox{}

\bigskip

\kotae{\sin 30^\circ={1\over2},\ \sin 45^\circ={1\over\sqrt{2}},\ 
	\sin 60^\circ={\sqrt{3}\over2}\ 
	{\sqrt{3}\over2},\ {1\over\sqrt{2}},\ {1\over2} \ 
	{1\over\sqrt{3}},\ 1,\ \sqrt{3}}

%\vskip3zh
\vfill

\begin{minipage}[t]{0.24\textwidth}
{\large ■ \(120^\circ\) の三角比}

\vskip2ex

\begin{tikzpicture}[rotate=0, scale=1, >=stealth, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1.732,1);
\draw[->] (-1.8,0)--(1.8,0);
\draw[->] (0,-0.5)--(0,2);
\draw(0,0)--(120:2);
\draw[->](0.3,0) arc (0:120:0.3);
\draw(45:0.6) node{$120^\circ$};
\filldraw(120:2) circle (1pt);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-0.2,-0.2) node {O};
\draw(2,-0.2) node {$x$};
\draw(-0.2,2) node {$y$};
\foreach \x in {1,-1}{\draw(\x,-0.3) node {$\x$};}
\draw(-0.2,1) node {$1$};
%\draw(5,-0.3) node {\tiny $5$};
\foreach \x in {-1,1}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}

\vspace*{-40mm}
\hspace*{40mm}
\begin{minipage}[t]{50mm}
\quad\makebox[11ex][l]{\(\sin 120^\circ=\)} \sikaku

\quad\makebox[11ex][l]{\(\cos 120^\circ=\)} \sikaku

\quad\makebox[11ex][l]{\(\tan 120^\circ=\)} \sikaku
\end{minipage}
\end{minipage}
%%%%\hskip3zw
\begin{minipage}[t]{0.24\textwidth}
{\large ■ \(135^\circ\) の三角比}

\vskip2ex

\begin{tikzpicture}[rotate=0, scale=1, >=stealth, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1.732,1);
\draw[->] (-1.8,0)--(1.8,0);
\draw[->] (0,-0.5)--(0,2);
\draw(0,0)--(135:1.414);
\draw[->](0.3,0) arc (0:135:0.3);
\draw(45:0.6) node{$135^\circ$};
\filldraw(135:1.414) circle (1pt);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-0.2,-0.2) node {O};
\draw(2,-0.2) node {$x$};
\draw(-0.2,2) node {$y$};
\foreach \x in {1,-1}{\draw(\x,-0.3) node {$\x$};}
\draw(-0.2,1) node {$1$};
%\draw(5,-0.3) node {\tiny $5$};
\foreach \x in {-1,1}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}

\vspace*{-40mm}
\hspace*{40mm}
\begin{minipage}[t]{50mm}
\quad\makebox[11ex][l]{\(\sin 135^\circ=\)} \sikaku

\quad\makebox[11ex][l]{\(\cos 135^\circ=\)} \sikaku

\quad\makebox[11ex][l]{\(\tan 135^\circ=\)} \sikaku
\end{minipage}
\end{minipage}

\bigskip

\bigskip

\begin{minipage}[t]{0.24\textwidth}
{\large ■ \(150^\circ\) の三角比}

\vskip2ex

\begin{tikzpicture}[rotate=0, scale=1, >=stealth, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1.732,1);
\draw[->] (-1.8,0)--(1.8,0);
\draw[->] (0,-0.5)--(0,2);
\draw(0,0)--(150:2);
\draw[->](0.3,0) arc (0:150:0.3);
\draw(45:0.6) node{$150^\circ$};
\filldraw(150:2) circle (1pt);
%\foreach \x in {-4,...,4}{\foreach \y in {-6,...,6}{\fill (\x,\y) circle (2pt);}}
\draw(-0.2,-0.2) node {O};
\draw(2,-0.2) node {$x$};
\draw(-0.2,2) node {$y$};
\foreach \x in {1,-1}{\draw(\x,-0.3) node {$\x$};}
\draw(-0.2,1) node {$1$};
%\draw(5,-0.3) node {\tiny $5$};
\foreach \x in {-1,1}{\draw(\x,-0.05)--(\x,0.05);}
\foreach \x in {1}{\draw(-0.05,\x)--(0.05,\x);}
%\draw(-1.2,-0.5) node {\tiny \( \scriptstyle {3-\sqrt{17}\over 4} \)};
%\draw(2.5,-0.5) node {\tiny \( \scriptstyle {3+\sqrt{17}\over 4} \)};
\end{tikzpicture}

\vspace*{-40mm}
\hspace*{40mm}
\begin{minipage}[t]{50mm}
\quad\makebox[11ex][l]{\(\sin 150^\circ=\)} \sikaku

\quad\makebox[11ex][l]{\(\cos 150^\circ=\)} \sikaku

\quad\makebox[11ex][l]{\(\tan 150^\circ=\)} \sikaku
\end{minipage}
\end{minipage}
\begin{minipage}[t]{70mm}

\kotae{\sin 120^\circ={\sqrt{3}\over2},\cos 120^\circ={-1\over2},\tan 120^\circ=-\sqrt{3} }

\bigskip

\kotae{\sin 135^\circ={1\over\sqrt{2}},\cos 135^\circ={-1\over\sqrt{2}},\tan 135^\circ=-1 }

\bigskip

\kotae{{\,1\,\over2},{-\sqrt{3}\over2},{1\over-\sqrt{3}} }


\end{minipage}



\vfill



\ifnum\make_pdf_with_insatsu>0
	\rotatebox{180}{{\normalsize\gtfamily\bfseries プリント\#61}\scriptsize
	{\normalsize\ajKaku{3}}~
	\ajKakko{1}~\( 5 \)\ 
	\ajKakko{2}~\( \frac{7\sqrt{2}}{2} \)\ 
	{\normalsize\ajKaku{4}}~
	\ajKakko{1}~\( \sqrt{21} \)\ 
	\ajKakko{2}~\( \sqrt{5} \)\ 
	{\normalsize\ajKaku{5}}~
	\ajKakko{1}~\( 5\sqrt{2} \)\ 
	\ajKakko{2}~\( 6 \)\ 
	{\normalsize\ajKaku{6}}~
	\ajKakko{1}~\( 13 \)\ 
	\ajKakko{2}~\( 10\sqrt{3} \)\ 
	\ajKakko{3}~\( \sqrt{5} \)\ 
	\ajKakko{4}~\( \sqrt{6} \)\ 
	{\normalsize\ajKaku{7}}~
	\ajKakko{1}~\( 60^\circ \)\ 
	\ajKakko{2}~\( 135^\circ \)
	}
\fi




\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

{\large\gtfamily\bfseries ■　三角形の面積}

\vspace*{-5ex}
\begin{center}
\begin{minipage}[t]{0.4\textwidth}
\begin{shadebox}
\vspace*{-9pt}
\[（三角形の面積）= {\,1\, \over 2}\times （辺の長さ）\times （辺の
長さ）\times \sin （間の角度）\]
\vspace*{-12pt}
\end{shadebox}
\end{minipage}
\end{center}


\toi 次の三角形の面積を求めなさい。

\nidangumi{\subtoi
\begin{tikzpicture}[rotate=30, scale=0.36, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (45:9);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-60,in=240] node [inner sep=0pt, fill=white]{\small $4$} (B);
\draw[dashed] (A) to[out=70,in=200] node [inner sep=2pt, fill=white]{\small $9$} (C);
\draw(A) +(48pt,12pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{9\sqrt{2}}
}%
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.6, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at ($ ({4-3*cos(60)},{3*sin(60)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (B) circle (12pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $4$} (B);
\draw[dashed] (B) to[out=90,in=-30] node [inner sep=2pt, fill=white]{\small $3$} (C);
\draw(B) +(-24pt,12pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}\kotae{3\sqrt{3}}
}%



\vfill


\ifnum\make_pdf_with_insatsu=0
	\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi

{\large\gtfamily\bfseries ■　正弦定理}

\vspace*{-5ex}
\begin{center}
\begin{minipage}[t]{0.4\textwidth}
\begin{shadebox}
\vspace*{-9pt}
\[ {\textcolor{blue}{\textgt{\bfseries 角度の向かい側にある辺の長さ}} \over \sin\textcolor{blue}{\textgt{\bfseries 角度}}}=
{\textcolor{red}{\textgt{\bfseries 角度の向かい側にある辺の長さ}} \over \sin\textcolor{red}{\textgt{\bfseries 角度}}}\]
\vspace*{-12pt}
\end{shadebox}
\end{minipage}
\end{center}

\toi 次の三角形の辺の長さ$x$を求めなさい。

\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.5, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at ($ ({3/sin(30)*sin(105)},0) $);
\coordinate (C) at ($ ({3/sin(30)*sin(105)-3*cos(45)},{3*sin(45)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\draw (B) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=80,in=180] node [inner sep=2pt, fill=white]{\small $x$} (C);
\draw[dashed] (C) to[out=0,in=100] node [inner sep=2pt, fill=white]{\small $3$} (B);
\draw(A) +(48pt,12pt) node{\footnotesize $30^\circ$};
\draw(B) +(-36pt,12pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{3\sqrt{2}}
}
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.8, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at ($ ({2/sin(45)*sin(75)},0) $);
\coordinate (C) at (60:2);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (9pt);
\draw (B) circle (9pt);
\end{scope}
\draw[dashed] (A) to[out=90,in=190] node [inner sep=2pt, fill=white]{\small $2$} (C);
\draw[dashed] (C) to[out=-10,in=90] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(A) +(20pt,6pt) node{\footnotesize $60^\circ$};
\draw(B) +(-20pt,6pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{\sqrt{6}}
}


\vfill
\vfill
\vfill

\newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

{\large\gtfamily\bfseries ■　正弦定理（外接円の半径）}

\vspace*{-5ex}
\begin{center}
\begin{minipage}[t]{0.3\textwidth}
\begin{shadebox}
\vspace*{-6pt}
\[ {\textcolor{red}{\textgt{\bfseries 角度の向かい側にある辺の長さ}} \over
	\sin\textcolor{red}{\textgt{\bfseries 角度}}}= 2R \]
\vspace*{-2ex}
\end{shadebox}
\end{minipage}
\end{center}


\toi 次の三角形の外接円の半径$R$を求めなさい。

\nidangumi{\subtoi 
\begin{tikzpicture}[scale=0.6, baseline=(current bounding box.north), >=stealth]
\coordinate (O) at (0,0);
\coordinate (C) at (-60:1.6);
\coordinate (B) at (-120:1.6);
\coordinate (A) at (70:1.6);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\fill[gray] (A) circle (5mm);
\end{scope}
\draw (O) circle (1.6);
\draw[line join=round] (A)--(B)--(C)--cycle;
%\fill (O) circle (1.5pt);
%\draw[dashed](O) -- (C);
%\draw(0.3,0) node{\small O};
\draw(A) ++(-3pt,-25pt) node{\tiny $30^\circ$};
\draw(-90:1.1) node{$5$};
%\draw(-50:0.8) node{\footnotesize $R$};
\end{tikzpicture}\kotae{5}
}{
\subtoi 
\begin{tikzpicture}[scale=0.8, >=stealth,
	baseline={([yshift=-11pt] current bounding box.north)}]
\coordinate (O) at (0,0);
\coordinate (C) at (0:1.6);
\coordinate (B) at (40:1.6);
\coordinate (A) at (-50:1.6);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\fill[gray] (C) circle (8pt);
\end{scope}
\draw (O) circle (1.6);
\draw[line join=round] (A)--(B)--(C)--cycle;
\draw(C)++(20pt,0) node{$135^\circ$};
\draw(0:0.5) node{$7$};
\end{tikzpicture}\kotae{\frac{7\sqrt{2}}{2}}
}


\vskip0.03\textheight


\ifnum\make_pdf_with_insatsu=0
	\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi


{\large\gtfamily\bfseries ■　余弦定理}

\vspace*{-2ex}
\begin{center}
\begin{minipage}[c]{0.34\textwidth}
\begin{shadebox}
\vspace*{-12pt}
\[	\left({角度の向かい \atop 側の辺の長さ}\right)^2 =
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=blue, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};^2+
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=red, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};^2-2\times
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=blue, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};\times
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=red, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};\times\cos (間の角度)
\]
\vspace*{-12pt}
\end{shadebox}
\end{minipage}
\end{center}


\toi 次の三角形の辺の長さ$x$を求めなさい。

\nidangumi{\subtoi %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=-130, scale=0.4, baseline={([yshift=-11pt] current bounding box.north)}]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at (60:4);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (20pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(2.5,-0.5) node[inner sep=1pt]{\small $5$};
%\draw(75:2) node[inner sep=1pt]{\small $4$};
%\draw(30:4.3) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $5$} (B);
\draw[dashed] (A) to[out=90,in=210] node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw[dashed] (C) to[out=0,in=100] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(25:48pt) node[inner sep=1pt]{\small $60^\circ$};
\end{tikzpicture}\kotae{\sqrt{21}}
}%
{\subtoi %
\begin{tikzpicture}[rotate=0, scale=1, baseline={([yshift=-11pt] current bounding box.north)}]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (3,0);
\coordinate (C) at ($ (135:{sqrt(2)})+(3,0) $);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (B) circle (9pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(1.5,-0.3) node[inner sep=1pt]{\small $3$};
%\draw(2.8,0.7) node[inner sep=1pt]{\small $\sqrt{2}$};
%\draw(35:1.2) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $3$} (B);
\draw[dashed] (A) to[out=45,in=180] node [inner sep=2pt, fill=white]{\small $x$} (C);
\draw[dashed] (C) to[out=0,in=90] node [inner sep=0pt, fill=white]{\small $\sqrt{2}$} (B);
\draw(B) ++(-16pt,6pt) node[inner sep=1pt]{\small $45^\circ$};
\end{tikzpicture}\kotae{\sqrt{5}}
}


\vfill
\vfill


\ifnum\make_pdf_with_insatsu=0
	\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi




\toi 次の三角形の面積を求めなさい。

\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.4, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at (135:4);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $5$} (B);
\draw[dashed] (A) to[out=170,in=280] node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw(A) +(3pt,32pt) node{\footnotesize $135^\circ$};
\end{tikzpicture}\kotae{5\sqrt{2}}
}
{\subtoi
\begin{tikzpicture}[rotate=30, scale=0.4, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (6,0);
\coordinate (C) at (150:4);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $6$} (B);
\draw[dashed] (A) to[out=180,in=290] node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw(A) +(3pt,18pt) node{\footnotesize $150^\circ$};
\end{tikzpicture}\kotae{6}
}


\vfill


\ifnum\make_pdf_with_insatsu>0
	\rotatebox{180}{{\normalsize\gtfamily\bfseries プリント\#61}\scriptsize
	\quad\( \sin 30^\circ={1\over2},\ \sin 45^\circ={1\over\sqrt{2}},\ 
	\sin 60^\circ={\sqrt{3}\over2},
	{\sqrt{3}\over2},{1\over\sqrt{2}},{1\over2},
	{1\over\sqrt{3}},1,\sqrt{3}\quad
	\sin 120^\circ={\sqrt{3}\over2},\cos 120^\circ={-1\over2},
	\tan 120^\circ=-\sqrt{3},
	{1\over\sqrt{2}},{-1\over\sqrt{2}},-1,
	{\,1\,\over2},{-\sqrt{3}\over2},{1\over-\sqrt{3}} \) \ 
	{\normalsize\ajKaku{1}}~\ajKakko{1}~\( 9\sqrt{2} \)\ \ajKakko{2}~\( 3\sqrt{3} \)\ 
	{\normalsize\ajKaku{2}}~\ajKakko{1}~\( 3\sqrt{2} \)\ \ajKakko{2}~\( \sqrt{6} \)\ 
	}
\fi



\newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\toi 次の三角形の辺の長さ$x$を求めなさい。（正弦定理と余弦定理が混じってます）


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=-150, scale=0.28, baseline={([yshift=-11pt] current bounding box.north)}]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (7,0);
\coordinate (C) at (120:8);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (20pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(3.5,-0.5) node[inner sep=1pt]{\small $7$};
%\draw(130:4) node[inner sep=1pt]{\small $8$};
%\draw(70:4.7) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $7$} (B);
\draw[dashed] (A) to[out=160,in=270] node [inner sep=2pt, fill=white]{\small $8$} (C);
\draw[dashed] (C) to[out=-10,in=130] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(60:36pt) node[inner sep=1pt]{\small $120^\circ$};
\end{tikzpicture}\kotae{13}
}
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.18, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at ($ ({10/sin(30)*sin(120)},0) $);
\coordinate (C) at (30:10);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (64pt);
\draw (C) circle (32pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw[dashed] (C) to[out=0,in=120] node [inner sep=2pt, fill=white]{\small $10$} (B);
\draw(A) +(128pt,36pt) node{\footnotesize $30^\circ$};
\draw(C) +(0pt,-56pt) node{\footnotesize $120^\circ$};
\end{tikzpicture}\kotae{10\sqrt{3}}
}


\vfill



\ifnum\make_pdf_with_insatsu=0
	\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi



\nidangumi{\subtoi
%\begin{tikzpicture}[rotate=-155, scale=1.2, baseline={([yshift=-11pt] current bounding box.north)}]
\begin{tikzpicture}[rotate=0, scale=1.2, baseline={([yshift=-11pt] current bounding box.north)}]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (1,0);
\coordinate (C) at ($ (135:{sqrt(2)}) $);%(135:1.414);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (4pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(0.5,-0.2) node[inner sep=1pt]{\small $1$};
%\draw(150:0.7) node[inner sep=1pt]{\small $\sqrt{2}$};
%\draw(90:0.7) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-40,in=220] node [inner sep=2pt, fill=white]{\small $1$} (B);
\draw[dashed] (A) to[out=180,in=270] node [inner sep=2pt, fill=white]{\small $\sqrt{2}$} (C);
\draw[dashed] (C) to[out=0,in=120] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(70:8pt) node[inner sep=1pt]{\small $135^\circ$};
\end{tikzpicture}\kotae{\sqrt{5}}
}
{\subtoi
\begin{tikzpicture}[rotate=0, scale=1, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at ($ ({3/sin(120)*sin(45)},0) $);
\coordinate (C) at ($ (120:{3/sin(120)*sin(15)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (4pt);
\draw (C) circle (6pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw[dashed] (C) to[out=10,in=135] node [inner sep=2pt, fill=white]{\small $3$} (B);
\draw(A) +(12pt,6pt) node{\footnotesize $120^\circ$};
\draw(C) +(12pt,-8pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{\sqrt{6}}
}



\vfill


\ifnum\make_pdf_with_insatsu=0
	\newpage%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi


{\large\gtfamily\bfseries ■　余弦定理}

\vspace*{-2ex}
\begin{center}
\begin{minipage}[c]{0.34\textwidth}
\begin{shadebox}
\vspace*{-12pt}
\[	\left({角度の向かい \atop 側の辺の長さ}\right)^2 =
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=blue, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};^2+
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=red, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};^2-2\times
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=blue, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};\times
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=red, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};\times\cos (間の角度)
\]
\vspace*{-12pt}
\end{shadebox}
\end{minipage}
\end{center}


\toi 次の三角形で\(\angle{\rm A}\)の大きさを求めなさい。

\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.4, >=stealth,
	baseline={([yshift=-16pt] current bounding box.north)}]
\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (B) at (8,0);
\coordinate (C) at (60:5);
\draw (A)--(B)--(C)--cycle;
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=90,in=200] node [inner sep=0pt, fill=white]{\small $5$} (C);
\draw[dashed] (A) to[out=-20,in=200] node [inner sep=1pt, fill=white]{\small $8$} (B);
\draw[dashed] (C) to[out=0,in=110] node [inner sep=0pt, fill=white]{\small $7$} (B);
\end{tikzpicture}\kotae{60^\circ}
}
{\subtoi
\begin{tikzpicture}[rotate=0, scale=1.5, >=stealth, baseline=(current bounding box.north)]
\coordinate (C) at (0,0);
\coordinate [label=below right:{\footnotesize A}] (A) at (1,0);
%\coordinate (C) at ($ ({(b^2+c^2-a^2)/(2*c)},{b*sqrt(1-((b^2+c^2-a^2)/(2*b*c)))}) $);
\coordinate (B) at ($ ({(sqrt(5)^2+1^2-sqrt(2)^2)/(2*1)},{sqrt(5)*sqrt(1-((sqrt(5)^2+1^2-sqrt(2)^2)/(2*sqrt(5)*1)))}) $);
\draw (A)--(B)--(C)--cycle;
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (5pt);
\end{scope}
\draw[dashed] (A) to[out=10,in=260] node [inner sep=0pt, fill=white]{\small $\sqrt{2}$} (B);
\draw[dashed] (A) to[out=210,in=-30] node [inner sep=1pt, fill=white]{\small $1$} (C);
\draw[dashed] (C) to[out=40,in=180] node [inner sep=0pt, fill=white]{\small $\sqrt{5}$} (B);
\end{tikzpicture}\kotae{135^\circ}
}


\vfill






\end{document}
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