angle of depression and angle of elevation angle of depression and angle of elevation angle of depression and angle of elevation

1. Directions: Determine whether the following statements represent an
Angle of Elevation or Angle of Depression.
1. Two points on the same side of a tree are
19.8 m apart. Their angles to the top of the tree are 21o11’ from one
point and 16o17’ from the other point.
2. The angle of a boy standing from a point
on a lighthouse 30.5 m above from the surface of the water makes an
angle of 3o17’with the sea.
3. A bird sits on top of a 5-meter lamppost.
The angle from the bird to the feet of an observer standing away from
the lamppost is 35o22’.
4. A stargazer saw the planet Jupiter at
midnight and assumed that his angle to the planet in the sky is 43o17’.
5. From an airplane at an altitude of 1,200
meters, its angle in connection with a rock from the ground is 28o18’.

2. Solving Problems
Involving Angle of
Elevation

3. Learning objectives
At the end of this lesson the students will be
able to:
• solve problems involving angle of
elevation
• solve for the missing sides and angles of
right triangles using the angle of
elevation.

4. Example 1.
Solve the following problems.
1. A man standing outside of his house flew kites every
afternoon during ECQ. According to him, he used 1,250
meters of string to fly the kite. If the angle of elevation
of the kite to the ground is 43o15’. What is the distance
of the kite to the ground?
Solution:
sin 43𝑜15′ =
𝒙
𝟏𝟐𝟓𝟎
𝑥 = 1250(0.6852)
𝑥 = 1250 sin 43𝑜15′ 𝒙 = 𝟖𝟓𝟔. 𝟒𝟖 m

5. 2. The Philippine Arena, the world’s largest indoor
arena has a height of 65 meters. Suppose an observer
is standing 30 meters away from the entrance, what
would be his angle of elevation to the roof of the
arena?

6. Activity
Directions: Solve for the value of x. Give the lengths of
the sides in two decimal places.
1.
2.
x
15
55°
44
x
36°

7. For numbers 3 and 4, solve for θ and give the values of
the angle in degrees and minutes.
3. 4.
28
15
Ɵ
11
18
Ɵ
cos Ɵ =
15
28
Ɵ = 57°36’
tan Ɵ =
11
18
Ɵ = 31°26’

8. Activity
Direction: Solve the following problems.
1. The angle of elevation to the top of the flagpole is
34o from a point 48 meters from the base of the
flagpole. What is the height of the flagpole?
2. When the angle of elevation of the sun is 61o, the
building casts a horizontal shadow of 50 meters. How
high is the building?

9. Directions: Read each of the following carefully. Choose
the letter that corresponds to the correct answer.
1. A 37-ft pole casts a 21 ft. shadow. What is the angle
of elevation of the sun?
A. 60°11′
B. 60°25′
C. 60°35′
D. 60°
2. If a kite makes an angle of 39°30’ with the level
ground when a 460 feet of string is out. How high is
the kite?
A. 292.6 𝑓𝑡
B. 292.59 𝑓𝑡
C. 292 𝑓𝑡
D. 292.5 𝑓𝑡

10. 3. The angle of elevation of a building 80 meters high
from a man on the ground is 50°42’. How far is the
man from the building?
A. 65.46 𝑚
B. 65.4 𝑚
C. 65.48 𝑚
D. 65.49 𝑚
4. A 5-ft man casts a 10.8 ft. shadow from the sun. What
is the angle of elevation of the sun?
A. 25°
B. 24°55′
C. 24°51′
D. 24°50′

11. 5. A guy wire which is 14 meters long is fastened from
the ground to a pole 6.7 meters above the ground.
What is the angle of the wire that makes with the
ground?
A. 28°36′
B. 28°35
C. 28°40′
D. 28°