Chapter 8.4, Problem 44PPS

To determine

The solution of the given right triangle.

Answer to Problem 44PPS

  $\begin{array}{l}m\angle J=69\\ KL=20.5\\ m\angle K=21\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to the Pythagorean Theorem:

  $\begin{array}{l}KL=\sqrt{{\left(JK\right)}^2-{\left(JL\right)}^2}\\ KL=\sqrt{{\left(22\right)}^2-{\left(8\right)}^2}\\ KL=\sqrt{420}\\ KL=20.5\end{array}$

According to the definition of Sine:

  $\begin{array}{l}\sin K=\frac{8}{22}\\ m\angle K={\sin }^{-1}\frac{8}{22}\\ m\angle K=21\end{array}$

The acute angles of a right triangle are complementary.

  $\begin{array}{l}m\angle K+m\angle J=90\\ 21+m\angle J=90\\ m\angle J=90-21\\ m\angle J=69\end{array}$