Chapter 5.3, Problem 3CYP

To determine

To list: The angles and sides of $\Delta WXY$ in order from smallest to largest.

Answer to Problem 3CYP

The sides from shortest to longest are $\overline{WY}$ , $\overline{XY}$ , and $\overline{WX}$ , and the angles from smallest to largest are $\angle X$ , $\angle W$ , and $\angle Y$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

First find the missing angle measure using the Triangle Angle Sum Theorem.

  $\begin{array}{c}m\angle X=180-\left(51+90\right)\\ =180-141\\ =39°\end{array}$

So, the angles from smallest to largest are $\angle X$ , $\angle W$ , and $\angle Y$ . The sides opposite to these angles are $\overline{WY}$ , $\overline{XY}$ , and $\overline{WX}$ , respectively. So, the sides from smallest to largest are $\overline{WY}$ , $\overline{XY}$ , and $\overline{WX}$ .

Therefore, the sides from shortest to longest are $\overline{WY}$ , $\overline{XY}$ , and $\overline{WX}$ , and the angles from smallest to largest are $\angle X$ , $\angle W$ , and $\angle Y$ .