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:

$\frac{a}{\sin\alpha}=\frac{c}{\sin c}$

Substitute the values:

$\frac{a}{\sin18}=\frac{9.2}{\sin90}$

And solve for a:

$\begin{gathered} a=\sin18\times\frac{9.2}{\sin90} \\ a=2.8 \end{gathered}$

For b:

$\begin{gathered} \frac{b}{\sin\beta}=\frac{c}{\sin C} \\ \frac{b}{\sin72}=\frac{9.2}{\sin90} \\ b=\sin72\times\frac{9.2}{\sin90} \\ b=8.7 \end{gathered}$

Answer:

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