Question

Find the size of angle ABC, giving the answer in degrees to 1 decimal place.

Answer 1

ANSWER:

27.9°

STEP-BY-STEP EXPLANATION:

We can calculate the angle ABC, by means of the law of sine, which is the following:

$\frac{\sin a}{A}=\frac{\sin b}{B}=\frac{\sin c}{C}$

We apply in this case and we have the following equation:

$\frac{\sin(\text{CAB)}}{CB}=\frac{\sin (\text{ABC)}}{AC}$

We replace and calculate for ABC:

$\begin{gathered} \frac{\sin125}{14}=\frac{\sin (\text{ABC)}}{8} \\ \sin (\text{ABC)}=\frac{8\cdot\sin 125}{14} \\ \text{ABC}=\sin ^{-1}(0.468) \\ \text{ABC}=27.9\text{\degree} \end{gathered}$

The angle ABC is 27.9°