Chapter 10.2, Problem 24WE

To determine

To construct: the right triangle with hypotenuse of length $a$ and one leg of length $b$ .

Explanation of Solution

Given Information:

Given figure,

  

Calculation:

Procedure:

1. Draw a line $l$ .
2. Let $P$ be a point on the line.
3. Using $b$ as radius and $P$ as center draw two arcs intersecting the line $l$ . Let this points be $Q$ and $S$ .
4. Using $a$ as radius and $Q$ as center, draw an arc.
5. With same radius and $S$ as center, draw an arc intersecting the arc drawn using $Q$ as center. Label the point of intersection as $R$ .
6. Draw $\overline{PR}$ .
7. Draw $\overline{QR}$ .

Thus, triangle $PQR$ is obtained whose hypotenuse length is equal to $a$ and one leg is $b$ .

The figure drawn is shown below.