Question

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

Answer 1

27.9°

Explanation:

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

`(\sin a)/(A)=(\sin b)/(B)=(\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} (\sin125)/(14)=\frac{\sin (\text{ABC)}}{8} \\ \sin (\text{ABC)}=(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°