Chapter 8.5, Problem 27HP

To determine

To explain:

The method used to estimate the value angle of elevation and depression

Answer to Problem 27HP

Use $45°-45°-90°$ triangle theorem or $30°-60°-90°$ triangle theorem to estimate the value angle of elevation and depression

Explanation of Solution

According to $45°-45°-90°$ triangle theorem:

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

According to $30°-60°-90°$ triangle theorem:

In a triangle $45°-45°-90°$ , the legs are congruent $l$ is $\sqrt{3}$ times the length of the shorter leg and the length of the hypotenuse $h$ is $2$ times the length of a shorter leg.

Therefore, if one needs to identify that a right triangle has a $30°,60°,45°$ then one has to solve the triangle without using trigonometry functions.