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Finding a Shorter Side Theory
![\begin{multicols}{2} \textbf{Example 1}\\ Find the exact value of \(x\).\\ \begin{center} \begin{tikzpicture}[scale=0.15,line width=1pt] \coordinate (O) at (0,0); \coordinate (A) at (0,24); \coordinate (B) at (7,0); \draw[line width=1pt] (O)--(B)node[midway ,below] {\(x\)}--(A)node[right=2pt,midway]{25cm}--(O) node[midway,left] {24cm}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \end{tikzpicture} \end{center} \textbf{Example 1 solution}\\ \(\begin{aligned} x^2+24^2 & =25^2 \\ x^2 & =25^2-24^2 \\ & =625-576 \\ x^2 & =49 \\ x & =\sqrt{49} \\ & =\sqrt{7 \times 7} \\ \therefore x & =7 \text{ cm} \end{aligned}\) \columnbreak \textbf{Example 2}\\ Find the value of \(y\) correct to one decimal place\\ \begin{center} \begin{tikzpicture}[scale=0.5] \coordinate (O) at (0,0); \coordinate (A) at (0,5); \coordinate (B) at (-7.5,0); \draw[line width=1pt] (O)--(B)node[midway ,below] {\(y\)}--(A)node[left=4pt,midway]{9cm}--(O) node[midway,right] {5cm}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \end{tikzpicture} \end{center} \textbf{Example 2 solution}\\ \(\begin{aligned} y^2+5^2 & =9^2 \\ y^2 & =9^2-5^2 \\ y^2 & =81-25 \\ y^2 & =56 \\ y & =\sqrt{56} \\ y & =7.5\text{ cm} \end{aligned}\) \end{multicols}](/media/dgicapqo/9231.png)
NSW Y8 Maths Pythagoras Finding a Shorter Side
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Finding a Shorter Side - Video - Finding a Shorter Side - Example 1
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