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,

`(\sin A)/(a)=(\sin B)/(b)=(\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}=(\sin84.7^o)/(563)=(\sin5.7^o)/(c)`

Consider

`(\sin84.7^o)/(563)=(\sin5.7^o)/(c)`

Solve for c.

`\begin{gathered} c=(563\sin5.7^o)/(\sin84.7^o) \\ =56.157\text{ f}eet \end{gathered}`