Question

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

Answer 1

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}`