Pythagoras’ Theorem In Three Dimensions - Questions
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Question 1
31253
\(ABCDEFGH\) is a rectangular prism. \(HF=12\) units, \(FE=5\) units, \(CE=8\) units. Find the length of \(BF\)
\begin{align}
&\text{In } \triangle GHF: \\
&\begin{aligned}
GH&=5, HF=12 \\
GF^{2}&=5^{2}+12^{2} \\
GF&=13\quad (\text{Triangle: } 5,12,13)
\end{aligned}\\
&\text{In } \triangle GBF \\
&\begin{aligned}
GB&=8, G F=13 \\
BF^{2}&=8^{2}+13^{2} \\
&=233 \\
BF&=\sqrt{233}=15.3
\end{aligned}
\end{align}
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