1. CHAPTER 8: RIGHT TRIANGLES
8-6
THE SINE AND COSINE RATIOS

2. 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
Hypotenuse
Opposite Leg A
Adjacent Leg

3. 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
Hypotenuse
Opposite Leg A
Adjacent Leg

4. EXAMPLE Find the values of x and y to the nearest integer. x = 470
28° x
1000

5. EXAMPLE
Find x° correct to the nearest degree. 30 18 x°

6. EXAMPLE √21 Find the length of the altitude of ∆ABC. 48, 66, 665 5
√21
48, 66, 66 B C 4
Find the length of the altitude of ∆ABC.
Find the measure of the three angles of ∆ABC.

7. REVIEW
We have concluded the trigonometric ratios that are used commonly for right triangles:
Tangent = opposite / adjacent
Sine = opposite / hypotenuse
Cosine = adjacent / hypotenuse

8. Sin = opp. Cos = adj. Tan = opp.
SOHCAHTOA
SOHCAHTOA is an acronym that helps us to remember the right triangle trigonometric ratios:
SOHCAHTOA
Sin = opp. Cos = adj. Tan = opp.
hyp hyp. adj.

9. CLASSWORK/HOMEWORK 8.6 Assignment Pg. 313, Classroom Exercises 1-10
Pgs , Written Exercises 1-12, 14