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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.

in this image I have a question, I already know the answer, but I got it wrong, so-example-1
User Lemzwerg
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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}

User Npiv
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