Chapter 5.5, Problem 42E

To determine

To solve: The triangle described, given the triangle at the right. Round to the nearest tenth, if necessary

  $B={33}^{\circ },c=15.2$

Answer to Problem 42E

  $\angle C={90}^{\circ },\angle A={57}^{\circ },a=12.9,b=8.3$

Explanation of Solution

Given information: Triangle:

Calculation:

This is the sketch of the triangle. We are told c = 15.2 and $\angle B={33}^{\circ }$ and asked to solve for missing parts.

From angle B we have the hypotenuse so we need to find a or b first. Let’s find b .

  $\begin{array}{l}\sin {33}^{\circ }=\frac{b}{15.2}\\ b=\sin {33}^{\circ }\times 15.2=8.3\\ \cos {33}^{\circ }=\frac{a}{15.2}\\ a=\cos {33}^{\circ }\times 15.2=12.9\\ \angle A={90}^{\circ }-{33}^{\circ }={57}^{\circ }\end{array}$

Thus,

  $\angle C={90}^{\circ },\angle A={57}^{\circ },a=12.9,b=8.3$