L1 Terms Ratios Find Missing Side

Find the three basic trigonometric ratios in a right triangle.Use trigonometric ratios to find missing lengths.

Objectives

trigonometric ratiossinecosinetangent

Vocabulary

A trigonometric ratio is a ratio of the lengths of two sides in a right triangle. Three basic trigonometric ratios are sine, cosine, and tangent, abbreviated sin, cos, and tan, respectively.

Confused?

Here’s an acronym to help you remember the ratios

Sine = Opposite divided by Hypotenuse

Cosine = Adjacent divided by Hypotenuse

Tangent = Opposite divided by Adjacent

SOH CAH TOA

Example 1: Finding the Value of a Trigonometric Ratio

Find sin A, cos A and tan A.

A

BC

17

15

8

Sin ASin A

Cos A

Cos A

Tan ATan A

COMMON ERRORALERT

Students tend to make simple mistakes bymislabeling the adjacent and opposite sides

To overcome this mistake first determine theHypotenuse (should be easy right?)

Then determine the opposite side (across fromthe angle referred to.)

The remaining side is the adjacent side.

Find each trigonometric ratio to the nearest thousandth.

Check It Out! Example 2

Sin BSin B =

Cos B

Cos B =

Tan BTan B =

To find trigonometric ratios on a graphing calculator, press and then the value of the degree. Be sure your calculator is in degrees.

Helpful Hint

Example 3: Application

A ladder is leaning against a wall. The base of the ladder makes a 60° angle with the ground. The base of the ladder is 17 feet from the wall. What is the length of the ladder?Draw a diagram to model the problem.

17 ft.60°

wallladder

A

A B

Cross multiply.

cos A =

The ladder is 34 feet long.

= 34

Check It Out! Example 4

Construction A 14-foot ladder is leaning against a building. The ladder makes a 70° angle with the ground. How far is the base of the ladder from the building? Round your answer to the nearest tenth of a foot.

Draw a diagram to model the problem.

cos A =x ft.

70°

wallladder(14 ft)

A B

cos 70° =

adjacent = 14(cos 70°) 4.8

The ladder’s base is about 4.8 feet from the building.

Multiply both sides by 14.

A

C B

2524

7

Take out a piece of paper.Write your name at the top.

Find each trigonometric ratio to the nearest thousandth.

1.Sin B2.Cos B3.Tan B