Trigonometry Tangent Ratio Flashcards

The tangent ratio is the ratio of the side _____ the acute angle over the side ______ to the acute angle.

The tangent of an angle is not which of the following?

The tangent ratio is used for _____ triangles.

A tangent ratio is greater than one.

A right triangle has an acute angle measure of 22°. Which two numbers represent the lengths of the legs of this triangle?

If sinA = 3/5 and cosA = 4/5, then what is tan A?

Find the measure of angle A when tan A = 32°.

If angles A and B are the acute angles of a right triangle and the tangent of A is 2.1445, then what is the measure of angle B?

Find the measure of angle A to the nearest degree.

Which option equals tan 40°? (Select all that apply)

The tangent of a 45 degree angle is _____.

Which of the following equations can be used to solve for x?

Find x to the nearest tenth.

Choose the triangle with x equal to 17.

Find the measure of angle A.

Tangent Ratio Basics

The tangent ratio compares the length of the side opposite an acute angle to the length of the side adjacent to the angle.
It is a fundamental concept applicable to right triangles.

Tangent Characteristics

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
The tangent ratio can vary, being greater than one depending on the angle.

Right Triangles

Tangent ratios are exclusively used in the context of right triangles, where at least one angle is acute.

Angle Measures and Calculations

For an acute angle of 22° in a right triangle, the legs can be represented by lengths of 2 and 5.
If sin A = 3/5 and cos A = 4/5, then tan A equals 3/4.
The tangent of a 45° angle is equal to 1, making it unique among angles.

Angle Measurement Problems

For specific angles based on given tangents, examples include finding angle A as 32° and another A measure as 63°.
If the tangent of angle A equals 2.1445, angle B is found to be 25°.

Solving for Unknowns

When given equations, such as tan20 = X/10, one can derive x to be approximately 18.7.
Equivalents for tan 40° include expressions like COS 50/SIN 50 and SIN 40/COS 40.

Special Cases

The tangent ratio can lead to various results in angle measurement scenarios and calculations, reflecting the relationship between angles and sides in right triangles.

Test your knowledge of the tangent ratio in trigonometry with these flashcards. Each card presents key concepts and definitions that are essential for understanding the relationship between angles and side lengths in triangles. Perfect for students looking to reinforce their understanding of tangent ratios.