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Round your answers to two significant digits. Write your answer for the angle measure in decimal degrees.

Round your answers to two significant digits. Write your answer for the angle measure-example-1

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Given the diagram, we have:


\alpha=180-90-72=18

Then, we use the law of sine:


(a)/(\sin\alpha)=(c)/(\sin c)

Substitute the values:


(a)/(\sin18)=(9.2)/(\sin90)

And solve for a:


\begin{gathered} a=\sin18*(9.2)/(\sin90) \\ a=2.8 \end{gathered}

For b:


\begin{gathered} (b)/(\sin\beta)=(c)/(\sin C) \\ (b)/(\sin72)=(9.2)/(\sin90) \\ b=\sin72*(9.2)/(\sin90) \\ b=8.7 \end{gathered}

Answer:


\begin{gathered} \alpha=18° \\ a=2.8 \\ b=8.7 \end{gathered}

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