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Constructing a Similar Triangle with a Scale Factor

Construct a t...

Question

Construct a triangle $A B C$ , in which $B C = 6 c m$ , $A B = 9 c m$ and angle $A B C = 60^{o}$ .

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Solution

$\begin{matrix} (o s (B) = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{9^{2} + 6^{2} - b^{2}}{2 \times 9 \times 6} = \frac{1}{2} 117 - b^{2} = 54 b^{2} = 63 b = 3 \sqrt{7} c m \end{matrix}$

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