Trigonometry Worksheets

**Page 1**

1.

Find the measure of angle θ in the figure.

a. | 48°42′ | ||

b. | 41°48′ | ||

c. | 33°41′ | ||

d. | 56°19′ |

In right triangle APQ,

tan θ =

θ = 33°41′.

Correct answer : (3)

2.

The angle of elevation of the top of a hill from the foot of a tower is 62° and the angle of elevation of the top of the tower from the foot of the hill is 28°. If the tower is 40 ft high, then find the height of the hill.

a. | 141ft | ||

b. | 11.3 ft | ||

c. | 101 ft. | ||

d. | 39.5 ft |

Draw the diagram.

Let

In right triangle QPA,

tan 28° =

In right triangle PAB, tan 62° =

The height of the hill is 141 ft.

Correct answer : (1)

3.

Tom and Sam are on either side of a tower of height $h$ meters.They measure the angle of elevation of the top of the tower as $\theta $ and $\phi $ respectively. Find the distance through which Tom and Sam are seperated. [Given $h$ = 160, $\theta $ = 50° and $\phi $ = 35°.]

a. | 302.71 meters | ||

b. | 160.61 meters | ||

c. | 84.57 meters | ||

d. | 363 meters |

Height of the pole is AB =

[Draw the diagram for the given data.]

[Write the angles of elevation of A from Tom, Sam.]

In the right triangle ADB, tan

[tan

BD =

[Substitute the value of tan 35° and find BD.]

In the right triangle ABC, tan

[tan

BC =

[Substitute the value of tan 50° and find BC.]

CD = CB + BD = 228.571 +134.340 » 363 m

[Use CD = CB + BD to find CD.]

So, the distance between Tom and Sam is 363 m.

Correct answer : (4)

4.

The angle of depression $\phi $ of the top of a tower of height $h$ meters from the top of another tower of height H meters is 25°. Find the horizontal distance between the two towers when $h$ = 93 and H = 125.

a. | 15 ft | ||

b. | 70 ft | ||

c. | 58 ft | ||

d. | 43 ft |

Height of the first tower is CD =

[Draw the diagram for the given data.]

Let the distance between the two towers, BC = ED =

The angle of depression of D from A is

[Write the angle of depression of D from A.]

[

In the right triangle ADE, tan

[Substitute the value of tan 25° and find

[From the figure AE = AB - BE =

32 = 0.46

[From step 6 and step 7.]

[Solve for

So, the distance between two towers is 70 meters.

Correct answer : (2)