Question

in this image I have a question, I already know the answer, but I got it wrong, so I want to work through the process to see what I did wrong.

Answer 1

Given that:

$\angle B=84.7^o,\angle C=5.7^o,AC=563\text{ f}eet$

Use the fact that the sum of the interior angles of a triangle is 180 degrees. So,

$\angle A+\angle B+\angle C=180^o^{}$

By using the sine rule,

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

where a is the side opposite to angle A, b is the side opposite to angle B and c is the side opposite to angle C.

Plug the given values.

$\frac{\sin A^{}}{a}=\frac{\sin84.7^o}{563}=\frac{\sin5.7^o}{c}$

Consider

$\frac{\sin84.7^o}{563}=\frac{\sin5.7^o}{c}$

Solve for c.

$\begin{gathered} c=\frac{563\sin5.7^o}{\sin84.7^o} \\ =56.157\text{ f}eet \end{gathered}$