Question

what is the measure of angle a in the triangle shown?
44 degrees
complete
which equation can you use to solve for b?
16/sin(44) = b/sin(54)
complete
to the nearest tenth, b ≈
done

Explanation:

Step1: Use the sine rule

The sine rule states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). In the given triangle, we have \(\frac{16}{\sin(44^{\circ})}=\frac{b}{\sin(54^{\circ})}\).

Step2: Solve for \(b\)

Cross - multiply the equation \(\frac{16}{\sin(44^{\circ})}=\frac{b}{\sin(54^{\circ})}\) to get \(b=\frac{16\times\sin(54^{\circ})}{\sin(44^{\circ})}\).
We know that \(\sin(44^{\circ})\approx0.6947\) and \(\sin(54^{\circ})\approx0.8090\).
Substitute the values: \(b = \frac{16\times0.8090}{0.6947}\).
First, calculate \(16\times0.8090 = 12.944\).
Then, \(b=\frac{12.944}{0.6947}\approx18.6\).

Answer:

\(18.6\)