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Algebraic

For the following exercises, use cofunctions of complementary angles.

cos ( 34° ) = sin ( __° )

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cos ( π 3 ) = sin (___)

π 6

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csc ( 21° ) = sec ( ___° )

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tan ( π 4 ) = cot ( __ )

π 4

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For the following exercises, find the lengths of the missing sides if side a is opposite angle A , side b is opposite angle B , and side c is the hypotenuse.

cos B = 4 5 , a = 10

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sin B = 1 2 ,   a = 20

b = 20 3 3 , c = 40 3 3

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tan A = 5 12 , b = 6

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tan A = 100 , b = 100

a = 10 , 000 , c = 10 , 000.5

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sin B = 1 3 ,   a = 2

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a = 5 , A = 60

b = 5 3 3 , c = 10 3 3

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c = 12 , A = 45

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Graphical

For the following exercises, use [link] to evaluate each trigonometric function of angle A .

A right triangle with sides 4 and 10 and angle of A labeled.

For the following exercises, use [link] to evaluate each trigonometric function of angle A .

A right triangle with sides of 10 and 8 and angle of A labeled.

For the following exercises, solve for the unknown sides of the given triangle.

Technology

For the following exercises, use a calculator to find the length of each side to four decimal places.

A right triangle with sides of 7, b, and c. Angles of 35 degrees and B are also labeled.

b = 9.9970 ,   c = 12.2041

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A right triangle with sides a, b, and 12. Angles of 10 degrees and B are also labeled.

a = 2.0838 ,   b = 11.8177

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b = 15 , B = 15

a = 55.9808 , c = 57.9555

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c = 200 , B = 5

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c = 50 , B = 21

a = 46.6790 , b = 17.9184

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a = 30 , A = 27

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b = 3.5 , A = 78

a = 16.4662 , c = 16.8341

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Extensions

A radio tower is located 400 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 36° , and that the angle of depression to the bottom of the tower is 23° . How tall is the tower?

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A radio tower is located 325 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 43° , and that the angle of depression to the bottom of the tower is 31° . How tall is the tower?

498.3471 ft

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A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 15° , and that the angle of depression to the bottom of the tower is . How far is the person from the monument?

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A 400-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 18° , and that the angle of depression to the bottom of the tower is . How far is the person from the monument?

1060.09 ft

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There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the top of the building is measured to be 40° . From the same location, the angle of elevation to the top of the antenna is measured to be 43° . Find the height of the antenna.

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There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 36° . From the same location, the angle of elevation to the top of the lightning rod is measured to be 38° . Find the height of the lightning rod.

27.372 ft

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Real-world applications

A 33-ft ladder leans against a building so that the angle between the ground and the ladder is 80° . How high does the ladder reach up the side of the building?  

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Practice Key Terms 5

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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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