Question

Given ∆ABC with Angle B = 84°, C = 32° and Side BC = 25. Find AC. Round to nearest integer

Answer 1

First, we have to make a diagram to visualize the problem.

First, we find angle A using the interior angle theorem.

$\begin{gathered} A+B+C=180 \\ A+84+32=180 \\ A=180-84-32 \\ A=64 \end{gathered}$

Then, we use the law of sines.

$\begin{gathered} \frac{AC}{\sin84}=\frac{BC}{\sin A} \\ \frac{AC}{\sin84}=\frac{25}{\sin 64} \\ AC=\frac{25\cdot\sin 84}{\sin 64}_{} \\ AC\approx28 \end{gathered}$

Therefore, AC is 28 units long.