Question

18 multiple choice 2 points for the triangle shown below, find b if ∠b = 75° and c = 15. (round your answer to the nearest tenth.) 14.5 14.7 14.3 14.9

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin B=\frac{b}{c}\). Given \(B = 75^{\circ}\) and \(c = 15\).

Step2: Solve for \(b\)

Since \(\sin B=\frac{b}{c}\), then \(b=c\times\sin B\). Substitute \(c = 15\) and \(B = 75^{\circ}\) into the formula. We know that \(\sin75^{\circ}=\sin(45^{\circ}+30^{\circ})=\sin45^{\circ}\cos30^{\circ}+\cos45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\approx0.966\). So \(b = 15\times\sin75^{\circ}\approx15\times0.966 = 14.5\)

Answer:

14.5