Question

Give. ∆ABC Angle B = 42°, Angle C = 71° and BC = 22. Find AB and round your answer to nearest integer.

Answer 1

Let's make a diagram to visualize the problem.

First, let's find angle A.

`\begin{gathered} A+B+C=180 \\ A+42+71=180 \\ A=180-71-42 \\ A=67 \end{gathered}`

Then, we use the law of sines to find AB.

`\begin{gathered} (AB)/(\sin71)=(BC)/(\sin A) \\ (AB)/(\sin71)=(22)/(\sin 67) \\ AB=(22\cdot\sin 71)/(\sin 67) \\ AB\approx23 \end{gathered}`

Therefore, AB is 23 units long, approximately.