1. From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the tower?

8028˚

x

Using the 28˚ angle as a reference, we know opposite and adjacent sides.

Use tan 28˚ = x80

oppadj

80 (tan 28˚) = x80 (.5317) = x x ≈ 42.5 About 43 m

tan

2. A ladder that is 20 ft is leaning against the side of a building. If the angle formed between the ladder and ground is 75˚, how far will Coach Jarvis have to crawl to get to the front door when he falls off the ladder (assuming he falls to the base of the ladder)?

ladde

r

building20

x75˚

Using the 75˚ angle as a reference, we know hypotenuse and adjacent side.

Use cos 75˚ = x20

adjhyp

20 (cos 75˚) = x20 (.2588) = x x ≈ 5.2 About 5 ft.

cos

4. A kite is flying at an angle of elevation of about 55˚. Ignoring the sag in the string, find the height of the kite if 85m of string have been let out.

string

85x

55˚

kite

Using the 55˚ angle as a reference, we know hypotenuse and opposite side.

Use sin 55˚ = x85

opphyp

85 (sin 55˚) = x85 (.8192) = x x ≈ 69.6 About 70 m

sin

5. A 5.50 foot person standing 10 feet from a street light casts a 24 foot shadow. What is the height of the streetlight?

5.5 14 shadow

x˚

tan x˚ = 5.514

x° ≈ 21.45°About 9 ft.

tan 21.4524

height

10

6. The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder?

25

x

angle of depression38º

38º

Using the 38˚ angle as a reference, we know opposite and adjacent side.

Use tan 38˚ = 25/x oppadj

(.7813) = 25/xX = 25/.7813 x ≈ 32.0 About 32 m

tan

Alternate Interior Angles are congruent