Chapter 8.4, Problem 43PPS

To determine

The solution of the given right triangle.

Answer to Problem 43PPS

  $\begin{array}{l}XZ=9.8\\ m\angle W=33\\ XW=15.1\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

The acute angles of a right triangle are complementary.

  $\begin{array}{l}m\angle Z+m\angle W=90\\ 57+m\angle W=90\\ m\angle W=90-57\\ m\angle W=33\end{array}$

According to the definition of Sine:

  $\begin{array}{l}\sin 57°=\frac{XW}{18}\\ 18\sin 57°=XW\\ XW=15.1\end{array}$

According to the Pythagorean Theorem:

  $\begin{array}{l}XZ=\sqrt{{\left(ZW\right)}^2-{\left(WX\right)}^2}\\ XZ=\sqrt{{\left(18\right)}^2-{\left(15.1\right)}^2}\\ XZ=\sqrt{95.99}\\ XZ=9.8\end{array}$