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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