Chapter 10.8, Problem 7ST3

To determine

To construct: a right triangle with an acute angle congruent to $\angle 1$ and hypotenuse congruent to $\overline{BC}$ .

Explanation of Solution

Consider a long segment $\overline{BC}$ and acute $\angle 1$ .

Draw $\overline{XY}=\overline{BC}$ and $\angle X=\angle 1$ .

Construct the bisector of $\overline{XY}$ . From the midpoint construct an arc touching $x$ and $y$ .

Extend the side of $\angle X$ , such that it intersects the arc at $Z$ .

Draw $\overline{XZ},\overline{ZY}$

Here $\Delta XYZ$ is right angle triangle with $\overline{XY}$ as hypotenuse.

The figure is shown below: