Question

solve for b.
round your final answer
to the nearest tenth.
law of sines: $\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}$

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(C\). Then \(C = 180^{\circ}-28^{\circ}-83^{\circ}=69^{\circ}\).

Step2: Apply the Law of Sines

According to the Law of Sines \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here \(a = 18\), \(A = 28^{\circ}\), \(B = 83^{\circ}\). So \(\frac{18}{\sin28^{\circ}}=\frac{b}{\sin83^{\circ}}\).
Cross - multiply to get \(b=\frac{18\times\sin83^{\circ}}{\sin28^{\circ}}\).
We know that \(\sin28^{\circ}\approx0.4695\) and \(\sin83^{\circ}\approx0.9925\).
Then \(b=\frac{18\times0.9925}{0.4695}=\frac{17.865}{0.4695}\approx38.0\).

Answer:

\(38.0\)