Chapter 8.4, Problem 65HP

To determine

To explain:

The use ratios of the side lengths to find out the angle measures of the acute angles in a right angle triangle

Answer to Problem 65HP

The measure of an acute angle of right angle triangle, use the trigonometric functions definitions to find the sine and cosine or tangent angle values.

Explanation of Solution

As per the definition of sine angle, if $\Delta ABC$ is right angle triangle with acute $\angle A$ , then the sine of $\angle A$ is the ratio of length of leg opposite $\angle A$ to the hypotenuse length.

As per definition of cosine angle, if $\Delta ABC$ is right angle triangle with acute $\angle A$ , then the cosine of $\angle A$ is the ratio of length of leg adjacent $\angle A$ to the hypotenuse length.

And tangent definition is if $\Delta ABC$ is right angle triangle with acute $\angle A$ , then the tangent of $\angle A$ is the ratio of leg opposite $\angle A$ length to the leg adjacent $\angle A$ length.

The measure of an acute angle of right angle triangle, firstly use the trigonometric functions definitions to find the sine and cosine or tangent angle values.

By using calculator to corresponding values of inverse function of trigonometric and its result is measure of acute angle.