geometry help use the triangle to find sin t, cos t, sin g, and cos g. write your answer in simplest...

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GEOMETRY HELP Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. sin T = = 12 20 3 5 = opposite hypotenuse cos T = = 16 20 4 5 = adjacent hypotenuse sin G = = 16 20 4 5 = opposite hypotenuse cos G = = 12 20 3 5 = adjacent hypotenuse Quick Check Sine and Cosine Ratios LESSON 8-4 Additional Examples

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Page 1: GEOMETRY HELP Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. sin T = = 12 20 3535 = opposite hypotenuse

GEOMETRYHELP

Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms.

sin T = =1220

35=

oppositehypotenuse

cos T = =1620

45=

adjacenthypotenuse

sin G = =1620

45=

opposite hypotenuse

cos G = =1220

35=

adjacent hypotenuse

Quick Check

Sine and Cosine RatiosLESSON 8-4

Additional Examples

Page 2: GEOMETRY HELP Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. sin T = = 12 20 3535 = opposite hypotenuse

GEOMETRYHELP

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.

cos 35° =height

20 Use the cosine ratio.

height = 20 • cos 35° Solve for height.

The flagpole is about 16 ft tall.

Sine and Cosine RatiosLESSON 8-4

Additional Examples

Quick Check

20 35 Use a calculator.

Page 3: GEOMETRY HELP Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. sin T = = 12 20 3535 = opposite hypotenuse

GEOMETRYHELP

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 =1.54.0 0.375= Use the cosine ratio.

Use the inverse of the cosine.m A = cos–1(0.375)

Round to the nearest degree.m A 68

Sine and Cosine RatiosLESSON 8-4

Additional Examples

Use a calculator.0.375

Page 4: GEOMETRY HELP Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. sin T = = 12 20 3535 = opposite hypotenuse

GEOMETRYHELP

(continued)

To find m B, use the fact that the acute angles of a right triangle are complementary.

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

m A + m B = 90 Definition of complementary angles

Substitute.68 + m B 90

m B 22

Sine and Cosine RatiosLESSON 8-4

Additional Examples

Quick Check

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