8-3: Trigonometry Objectives To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles To use the sine,

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8-3: Trigonometry Objectives To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles

Trigonometry Ratios

Trigonometry: The study of the relationship between the sides and the angles of a triangle Hypotenuse Opposite Adjacent A B C Tangent of tan A = Sine of sin A = Cosine of cos A = SOH CAH TOA

S O H TOASOHCAH ineine ppositepposite ypotenuseypotenuse osineosine dJacentdJacent ypotenuseypotenuse T O A angentangent djacentdjacent ppositepposite

Examples 20 0 500 ft x 8 ft A 15 ft sin 20 0 = x (sin 20 0 ) = 500 x = x ≈ 1,462 ft tan A = tan A = 0.5333 p. 510: 1-6, 11-19 x = 35 0 872 SOH CAH TOA Calculators in “degree” mode!!

Using Inverses > You know two sides > You want to find the measure of one of the acute angles.

S O H TOASOHCAH ineine ppositepposite ypotenuseypotenuse osineosine dJacentdJacent ypotenuseypotenuse T O A angentangent djacentdjacent ppositepposite 8-3 DAY 2

20 0 500 ft x 8 ft A 15 ft sin 20 0 = x (sin 20 0 ) = 500 x = x ≈ 1,462 ft tan A = tan A = 0.5333 A = tan -1 0.5333 A ≈ 28 0 x = SOH CAH TOA

SOH CAH TOA B = cos -1 0.6631 500 ft 754 ft cos B = B B ≈ 48 0 p.511: 22-27, 34, 35, 59-62

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