CHAPTER 8:RIGHT TRIANGLES

8-6

THE SINE AND COSINE RATIOS

THE SINE RATIO

Given a right triangle, the sine is a ratio of the opposite leg and the hypotenuse.

Sine of A = leg opposite A / hypotenuse

A

Opposite Leg

Adjacent Leg

Hypotenuse

THE COSINE RATIO

Given a right triangle, the ratio of the adjacent leg to the hypotenuse is known as the cosine.

Cosine A = leg adjacent to A / hypotenuse

A

Opposite Leg

Adjacent Leg

Hypotenuse

EXAMPLEFind the values of x and y to the nearest

integer.

x = 470

y = 883

x

y

28°

1000

EXAMPLE

Find x° correct to the nearest degree.

x°

3018

EXAMPLE

1. Find the length of the altitude of ∆ABC.

2. Find the measure of the three angles of ∆ABC.

1. √21

2. 48, 66, 66

5 5

4

A

B C

REVIEW

We have concluded the trigonometric ratios that are used commonly for right triangles:

1. Tangent = opposite / adjacent

2. Sine = opposite / hypotenuse

3. Cosine = adjacent / hypotenuse

SOHCAHTOASOHCAHTOA is an acronym that helps us to

remember the right triangle trigonometric ratios:

SOHCAHTOA

Sin = opp. Cos = adj. Tan = opp.

hyp. hyp. adj.

CLASSWORK/HOMEWORK

8.6 Assignment• Pg. 313, Classroom Exercises 1-10

• Pgs. 314-315, Written Exercises 1-12, 14