Sine and Cosine Ratios LESSON 8-4 Additional Examples

Use the triangle to find sin

T

, cos

T

, sin

G

, and cos

G

. Write your answer in simplest terms.

sin

T

= opposite hypotenuse = 12 20 = 3 5 cos

T

= adjacent hypotenuse = 16 20 = 4 5 sin

G

= opposite hypotenuse = 16 20 = 4 5 cos

G

= adjacent hypotenuse = 12 20 = 3 5

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Sine and Cosine Ratios LESSON 8-4 Additional Examples

A 20 ft. wire supporting a flagpole forms a 35˚ angle with the flagpole. To the nearest foot, how high is the flagpole?

The flagpole, wire, and ground form a right triangle with the wire as the hypotenuse.

Because you know an angle and the measures of its adjacent side and the hypotenuse, you can use the cosine ratio to find the height of the flagpole.

20 cos 35 ° = height 20 height = 20 • cos 35° 35 Use the cosine ratio.

Solve for height.

Use a calculator.

The flagpole is about 16 ft tall.

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Sine and Cosine Ratios LESSON 8-4 Additional Examples

A right triangle has a leg 1.5 units long and hypotenuse 4.0 units long. Find the measures of its acute angles to the nearest degree.

Draw a diagram using the information given.

Use the inverse of the cosine function to find

m A

.

cos

A

= 1.5

4.0

= 0.375

m A

= cos –1 (0.375) 0.375

m A

68 Use the cosine ratio.

Use the inverse of the cosine.

Use a calculator.

Round to the nearest degree.

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Sine and Cosine Ratios LESSON 8-4 Additional Examples (continued)

To find

m B

, use the fact that the acute angles of a right triangle are complementary.

m A

+

m B

= 90 Definition of complementary angles 68 +

m B

90 Substitute.

m B

22 The acute angles, rounded to the nearest degree, measure 68 and 22.

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