\documentclass[11pt,b4j,dvipdfmx,landscape,twocolumn,papersize]{jsarticle}
% furikana.sty	http://xymtex.com/fujitas2/texlatex/index.html#tategumi
\usepackage{ascmac,bm,amssymb,furikana}
\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}

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\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）
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\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}

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\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<}}
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\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 \# 60}\hfill
年\hskip8ex 組\hskip8ex 号 \hskip5ex

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

\namae

\vskip-5ex

{\large\gtfamily\bfseries ■　余弦定理}{\large （\kana{余弦}{よげん}とは$\cos$のことです）}

\bigskip
　余弦定理を使うと『二辺とその間の角度』が分かったときの
『向かい側の辺の長さ』を計算することが出来る。

\vspace*{-5ex}
\begin{center}
\begin{minipage}[t]{0.4\textwidth}
\begin{shadebox}
\vspace*{-12pt}
\[	\left({角度の向かい \atop 側の辺の長さ}\right)^2 =
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=red, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};^2+
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=blue, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};^2-2\times
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=red, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};\times
	\tikz[baseline=1pt]\draw(3pt,3pt) node[circle, fill=blue, inner sep=1pt]{\small\textcolor{white}{\gtfamily\bfseries 辺}};\times\cos (間の角度)
\]
\vspace*{-12pt}
\end{shadebox}
\end{minipage}
\end{center}

\vspace*{-9pt}
\begin{minipage}[t]{0.33\textwidth}
\fbox{例題}\quad 右の三角形で，$x$の長さを求めなさい。

\quad
\fbox{解}\quad
余弦定理より

\vspace*{-9ex}
\begin{eqnarray*}
x^2 &=& 3^2+5^2-2\times3\times5\times\cos120^\circ \\
x^2 &=& 9+25 \boldsymbol{-2\times3\times5\times{\,-1\,\over2}} \\[-6pt]
x^2 &=& 9+25 \hooklen{{}-2\times3\times5\times{\,-1\,\over2}}
		{\boldsymbol{{}+15}} \\
x^2 &=& 49 \\
x &=& \pm\sqrt{7} \\
x>0だから\hskip1.5zw x&=& \sqrt{49}\\
x&=& 7 \quad\mbox{\□答}
\end{eqnarray*}
\end{minipage}
%\hskip3zw
%■ Tikz バージョン
\begin{tikzpicture}[rotate=0, 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 (3,0);
\coordinate (C) at (120:5);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $3$} (B);
\draw[dashed] (A) to[out=150,in=270] node [inner sep=2pt, fill=white]{\small $5$} (C);
\draw[dashed] (C) to[out=-10,in=120] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(50:32pt) node[inner sep=1pt]{\small $120^\circ$};
\end{tikzpicture}


%\bigskip

\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=-120, 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 (120:4);
\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(135:2) node[inner sep=1pt]{\small $4$};
%\draw(70:3) 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=150,in=270] node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw[dashed] (C) to[out=0,in=135] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(60:36pt) node[inner sep=1pt]{\small $120^\circ$};
\end{tikzpicture}\kotae{\sqrt{61}}
}%
{\subtoi %
%■ Tikz バージョン
\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}
}%

\vfill

\nidangumi{\subtoi %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=0, scale=0.6, 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 ($ (45:{2*sqrt(2)}) $);%    (45:2.828);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(1.5,-0.5) node[inner sep=1pt]{\small $3$};
%\draw(70:1.5) node[inner sep=1pt]{\small $2\sqrt{2}$};
%\draw(25:3.2) 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=90,in=180] node [inner sep=0pt, fill=white]{\small $2\sqrt{2}$} (C);
\draw[dashed] (C) to[out=-20,in=80] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(23:36pt) node[inner sep=1pt]{\small $45^\circ$};
\end{tikzpicture}\kotae{\sqrt{5}}
}
{\subtoi %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=0, scale=0.6, baseline={([yshift=-11pt] current bounding box.north)}]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (2,0);
\coordinate (C) at (60:3);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(1,-0.3) node[inner sep=1pt]{\small $2$};
%\draw(70:1.5) node[inner sep=1pt]{\small $3$};
%\draw(30:2.5) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=1pt, fill=white]{\small $2$} (B);
\draw[dashed] (A) to[out=90,in=210] node [inner sep=2pt, fill=white]{\small $3$} (C);
\draw[dashed] (C) to[out=-45,in=60] node [inner sep=2pt, fill=white]{\small $x$} (B);
\draw(30:32pt) node[inner sep=1pt]{\small $60^\circ$};
\end{tikzpicture}\kotae{\sqrt{7}}
}

\vfill



\ifnum\make_pdf_with_insatsu>0
	\rotatebox{0}{{\normalsize\gtfamily\bfseries プリント\#60}\scriptsize
	{\normalsize\ajKaku{1}} \ajKakko{1}~\( \sqrt{61} \)\ 
	\ajKakko{2}~\( 13 \)\ 
	\ajKakko{3}~\( \sqrt{5} \)\ \ajKakko{4}~\( \sqrt{7} \)\ 
	\ajKakko{5}~\( \sqrt{5} \)\ \ajKakko{6}~\( 2\sqrt{21} \)\ 
	\ajKakko{7}~\( \sqrt{7} \)\ \ajKakko{8}~\( 7 \)\ 
	{\normalsize\ajKaku{2}} \ajKakko{1}~\( 5 \) \quad \ajKakko{2}~\( 2 \)
	}
\fi


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

\nidangumi{\subtoi %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=-155, 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 $x$};
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\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 %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=45, 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 (6,0);
\coordinate (C) at ($ (135:{2*sqrt(3)}) $);%(135:3.464);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(3,-0.5) node[inner sep=1pt]{\small $6$};
%\draw(-1.4,0.5) node[inner sep=1pt]{\small $2\sqrt{3}$};
%\draw(60:2.2) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $6$} (B);
\draw[dashed] (A) to[out=180,in=280] node [inner sep=1pt, fill=white]{\small $2\sqrt{3}$} (C);
\draw[dashed] (C) to[out=0,in=150] node [inner sep=1pt, fill=white]{\small $x$} (B);
\draw(75:24pt) node[inner sep=1pt]{\small $150^\circ$};
\end{tikzpicture}\kotae{2\sqrt{21}}
}%

\vfill


\nidangumi{\subtoi %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=0, scale=0.6, baseline={([yshift=-11pt] 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 ($ (30:{sqrt(3)}) $);%(30:1.732);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (16pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(2,-0.5) node[inner sep=1pt]{\small $4$};
%\draw(60:0.8) node[inner sep=1pt]{\small $\sqrt{3}$};
%\draw(15:3) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=1pt, fill=white]{\small $4$} (B);
\draw[dashed] (A) to[out=90,in=150] node [inner sep=1pt, fill=white]{\small $\sqrt{3}$} (C);
\draw[dashed] (C) to[out=20,in=135] node [inner sep=1pt, fill=white]{\small $x$} (B);
\draw(15:36pt) node[inner sep=1pt]{\small $30^\circ$};
\end{tikzpicture}\kotae{\sqrt{7}}
}
{\subtoi %
%■ Tikz バージョン
%\begin{tikzpicture}[rotate=120, scale=0.4, baseline={([yshift=-11pt] current bounding box.north)}]
\begin{tikzpicture}[rotate=120, 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 (8,0);
\coordinate (C) at (60:3);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (16pt);
\end{scope}
\draw (A)--(B)--(C)--cycle;
%\draw[dashed, rounded corners=24pt] (A)--(1.5,-0.5)--(B);
%\draw(4,-0.5) node[inner sep=1pt]{\small $8$};
%\draw(75:1.5) node[inner sep=1pt]{\small $3$};
%\draw(20:5) node[inner sep=1pt]{\small $x$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=1pt, fill=white]{\small $8$} (B);
\draw[dashed] (A) to[out=110,in=180] node [inner sep=1pt, fill=white]{\small $3$} (C);
\draw[dashed] (C) to[out=10,in=135] node [inner sep=1pt, fill=white]{\small $x$} (B);
\draw(30:36pt) node[inner sep=1pt]{\small $60^\circ$};
\end{tikzpicture}\kotae{7}
}%

\vfill

\toi 次の三角形の辺の長さ$x$を求めなさい。（これは少し難しい。2次方程式を解かなければいけない）

\nidangumi{\subtoi %
%■ Tikz バージョン
\begin{tikzpicture}[rotate=-155, 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 (120:3);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (16pt);
\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 $x$};
%\draw(135:1.5) node[inner sep=1pt]{\small $3$};
%\draw(40:3) node[inner sep=1pt]{\small $7$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=1pt, fill=white]{\small $x$} (B);
\draw[dashed] (A) to[out=170,in=260] node [inner sep=1pt, fill=white]{\small $3$} (C);
\draw[dashed] (C) to[out=0,in=135] node [inner sep=1pt, fill=white]{\small $7$} (B);
\draw(60:36pt) node[inner sep=1pt]{\small $120^\circ$};
\end{tikzpicture}\kotae{5}
}%
{\subtoi %
%■ Tikz バージョン
\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 ($ ({sqrt(3)},0) $);%(1.732,0);
\coordinate (C) at (150:2);
\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(0.8,-0.3) node[inner sep=1pt]{\small $\sqrt{3}$};
%\draw(170:1) node[inner sep=1pt]{\small $2$};
%\draw(60:0.8) node[inner sep=1pt]{\small $\sqrt{13}$};
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=1pt, fill=white]{\small $\sqrt{3}$} (B);
\draw[dashed] (A) to[out=180,in=300] node [inner sep=1pt, fill=white]{\small $x$} (C);
\draw[dashed] (C) to[out=0,in=150] node [inner sep=0pt, fill=white]{\small $\sqrt{13}$} (B);
\draw(60:10pt) node[inner sep=1pt]{\small $150^\circ$};
\end{tikzpicture}\kotae{2}
}

\vspace*{5zh}
\vfill



\end{document}



