Question

Given ∆ABC Angle A = 65°, C = 100° and side BC= 20. Find AB and round the answer the nearest integer

Answer 1

22

Explanation:

With the data provided we can propose the following figure:

We can apply the law of sine as follows:

`\begin{gathered} (a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C) \\ \text{ in this case:} \\ (BC)/(\sin A)=(AB)/(\sin C) \end{gathered}`

Replacing and solving for AB:

`\begin{gathered} (20)/(\sin65)=(AB)/(\sin 100) \\ AB=20\cdot(\sin 100)/(\sin 65) \\ AB=21.7\cong22 \end{gathered}`

The value of AB is 22