Chapter 8.3, Problem 50HP

To determine

To explain:

The given statement.

Answer to Problem 50HP

The given statement is explained below.

Explanation of Solution

Given information:

Statement:

The lengths of the two legs of a $30°-60°-90°$ triangle in radical form if you are given the length of the hypotenuse.

In a $45°-45°-90°$ triangle, the legs $l$ are congruent and the length of the hypotenuse $h$ is $\sqrt{2}$ times the length of a leg.

In a $30°-60°-90°$ triangle, the length of the hypotenuse $h$ is $2$ times the length of the shorter leg $s$ , and the length of the longer leg $l$ is $\sqrt{3}$ times the length of the shorter leg.

Therefore, if one identifies that a right triangle has an $30°,60°,45°$ angle, then one could solve the triangle without using a calculator.