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} (AC)/(\sin84)=(BC)/(\sin A) \\ (AC)/(\sin84)=(25)/(\sin 64) \\ AC=(25\cdot\sin 84)/(\sin 64)_{} \\ AC\approx28 \end{gathered}`

Therefore, AC is 28 units long.