Question

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

Answer 1

ANSWER:

22

STEP-BY-STEP EXPLANATION:

With the data provided we can propose the following figure:

We can apply the law of sine as follows:

$\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \\ \text{ in this case:} \\ \frac{BC}{\sin A}=\frac{AB}{\sin C} \end{gathered}$

Replacing and solving for AB:

$\begin{gathered} \frac{20}{\sin65}=\frac{AB}{\sin 100} \\ AB=20\cdot\frac{\sin 100}{\sin 65} \\ AB=21.7\cong22 \end{gathered}$

The value of AB is 22