Chapter 6.1, Problem 54E

To determine

Tofind:Whether the law of Sines be used to solve a right angles triangle, if so then solve the triangle.

Explanation of Solution

Given: The given data is, $B=50°,C=90°,a=10$ .

If at least one side and one angle are given or two sides are given then the Law of sines can be used to solve a right triangle.

By the law of Sines

  $Area=\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

The measure of angle $A$ is calculated as,

  $\begin{array}{c}A=180°-90°-50°\\ =40°\end{array}$

The measure of side $c$ is calculated as,

  $\begin{array}{c}\frac{10}{\sin 40°}=\frac{c}{\sin 90°}\\ c=15.557\end{array}$

The measure of side $b$ is calculated as,

  $\begin{array}{c}\frac{10}{\sin 40°}=\frac{b}{\sin 50°}\\ b=11.918\end{array}$

Since, this is a right triangle. Once the two legs are obtained, then the Pythagorean Theorem can be used to find the hypotenuse.