1. 1. From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the tower?x
28˚ 80
Using the 28˚ angle as a reference, we know opposite and adjacent sides.
Use
tan
tan 28˚ =
80 (tan 28˚) = x
80 (.5317) = x
x ≈ 42.5
About 43 m

2. 2. A ladder that is 20 ft is leaning against the side of a building
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)? 20
building
ladder
75˚ x
Using the 75˚ angle as a reference, we know hypotenuse and adjacent side.
Use
cos
cos 75˚ =
20 (cos 75˚) = x
20 (.2588) = x
x ≈ 5.2
About 5 ft.

3. 4. A kite is flying at an angle of elevation of about 55˚
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.
kite 85 x
string
55˚
Using the 55˚ angle as a reference, we know hypotenuse and opposite side.
Use
sin
sin 55˚ =
85 (sin 55˚) = x
85 (.8192) = x
x ≈ 69.6
About 70 m

4. 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 x˚ 10 14
shadow
tan x˚ =
x° ≈ °
About 9 ft.

5. 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?
38º
angle of depression 25
Alternate Interior Angles are congruent
38º x
Using the 38˚ angle as a reference, we know opposite and adjacent side.
Use
tan
tan 38˚ = 25/x
(.7813) = 25/x
X = 25/.7813
x ≈ 32.0
About 32 m