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 Hypotenuse Opposite Leg A Adjacent Leg

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

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

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

EXAMPLE √21 Find the length of the altitude of ∆ABC. 48, 66, 66 5 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.

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

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.

CLASSWORK/HOMEWORK 8.6 Assignment Pg. 313, Classroom Exercises 1-10 Pgs. 314-315, Written Exercises 1-12, 14