Page 811 - Algebra 1

L E S S O N Using Trigonometric Ratios 117
Warm Up
New Concepts
1. Vocabulary A ratio is the comparison of two quantities using . (85)
2. If the two legs of a right triangle measure 9 inches and 12 inches, find the
(85)
length of the hypotenuse.
3. In a right triangle, one leg measures 10 inches and the hypotenuse measures
(85)
Decide if the following are Pythagorean triples or not. 4. 6, 10, 8 5. 8, 12, 20
(85) (85)
Recall that a right triangle has one right angle and two acute angles. In the triangle, ∠C is the right angle and ∠A and ∠B are the acute angles.
Using ∠A in the triangle, the leg across from the angle is called the opposite leg and the leg next to ∠A is called the adjacent leg. The hypotenuse is always opposite the right angle and is always the longest side of the triangle.
A
leg adjacent b c hypotenuse
to ∠A
CaB leg opposite ∠A
In any right triangle, there are six trigonometric ratios that can be written using two side lengths of the triangle in relation to the angles of the triangle. The three most common trigonometric ratios are sine, cosine, and tangent, abbreviated sin, cos, and tan, respectively.
17 inches. Find the length of the other leg.
Hint
The three trigonometric ratios of sine, cosine, and tangent can be remembered using the mnemonic device:
SOH-CAH-TOA
(pronounced “sew-ka- toe-a”). Sine equals Opposite leg over Hypotenuse, Cosine equals Adjacent leg
over Hypotenuse, and Tangent equals Opposite leg over Adjacent leg. This can also be written
as S_o C_a T_o . hha
Sine, Cosine, and Tangent
___
length of hypotenuse c
sine of ∠A = length of leg opposite ∠A = a
_
___
length of hypotenuse c
cosine of ∠A = length of leg adjacent to ∠A = b
_
___
length of leg adjacent to ∠A b
tangent of ∠A = length of leg opposite ∠A = a
_
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