Chapter 13.2, Problem 1E

Solution

To find: The missing length in $45°-45°-90°$ triangle if its hypotenuse is $1$ inch.

The side length of each leg of $45°-45°-90°$ triangle is $\frac{\sqrt{2}}{2}\text{ inch}$ .

Given:

The hypotenuse of $45°-45°-90°$ triangle is $1$ inch.

Concept used:

In $45°-45°-90°$ triangle, the sides opposite to angle $45°$ are equal and hypotenuse is written as $\sqrt{2}a$ if $\left(a\right)$ is the leg of triangle as shown below.

  

Calculation:

Since the hypotenuse of triangle is $1$ inch. Therefore, using the concept stated above if $\left(a\right)$ is the side length of each leg, then $\sqrt{2}a=1$ gives,

  $\begin{array}{c}a=\frac{1}{\sqrt{2}}\\ =\frac{\sqrt{2}}{2}\text{ inch}\mathrm{....}\left(\text{Rationalize}\right)\end{array}$

Hence the side length of each leg of $45°-45°-90°$ triangle is $\frac{\sqrt{2}}{2}\text{ inch}$ .

Conclusion:

The side length of each leg of $45°-45°-90°$ triangle is $\frac{\sqrt{2}}{2}\text{ inch}$ .