The document focuses on solving problems related to the angle of depression and right triangles. It includes learning objectives, examples, and activities that require calculating distances and angles based on given scenarios. Various problems are presented for practice, each requiring students to determine missing values in the context of real-world applications.

1. Activity No. Solve Me
Directions: Solve the following.
25
x
45°
28
15
Ɵ

2. Solving Problems
Involving Angle
of Depression

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

4. Examples: Solve the following.
1. An observer lying on the top of a hill in
Binangonan, Rizal is overlooking the view of Laguna
Lake. Suppose that the hill is 25 meters high, and the
angle of depression of the observer to the lakeshore
is 64o11’, what is the distance of the lakeshore to
the foot of the hill?

5. 2. A cat is seen looking at the window of a building. As
the cat looks downward, it saw a garbage can outside.
If the window where the cat is seen is 6 meters above
the ground and the garbage can is 2 meters away from
the base of the building, what is the angle of
depression of the cat to the garbage can?

6. Activity 2. Do it your Self!
Direction: Solve for the value of x. Give the lengths of
the sides in two decimal places. For numbers 3, 4, and
5, solve for θ and give the angle measures in degrees
and minutes.
1. 2.
x
15
27°
A
B C
19
x
18°
E
F
G

7. 27
19
Ɵ
H I
J
28
17
Ɵ
X
Y Z
19
12
Ɵ
L
M N
3. 4.
5.

8. Directions: Read each of the following carefully.
Choose the letter that corresponds to the correct
answer.
1.From the top of a mountain, 135 meters high, a
ship is seen below in the sea. It is observed that
the angle of depression of the ship is 21o. How far
is the ship from the top of the mountain?
A.376.71 𝑚
B.376 𝑚
C.376.72 𝑚
D.376.73 𝑚

9. 2. On the rooftop of a school building, an observer
saw a broken chair on the school ground 4 meters
away from the base of the building. What is the
angle of depression of the observer to the broken
chair if the building is 18 meters high?
A. 77𝑜38′ C. 77𝑜28′
B. 77𝑜18′ D. 77𝑜
3. A pilot on a plane saw a nearby island in front of
him. If he is 2975 m above the ground and the
horizontal distance of the island to the pilot 2345
m away. What is the angle of depression of the
pilot to the island?
A. 51𝑜45′ C. 51𝑜43′
B. 51𝑜40′ D. 51𝑜

10. 4. A boy is seen standing on the highest part of a
mango tree. On top of the tree, he saw an
observer looking at him 5 meters away. If the angle
of depression of the boy to the observer is 34o26’,
what is the height of the tree?
A. 3.44 𝑚 C. 3.42 𝑚
B. 3.4 𝑚 D. 3.43 𝑚
5. A man is seen on top of a coconut tree. 3 meters
away from him is another coconut tree. On the
bottom of the other tree, there is a fallen coconut.
If the angle of depression of the man to the fallen
coconut is 68o17’, how high is the coconut tree
that he is located?
A. 7.55 𝑚 C. 7.53 𝑚
B. 8 𝑚 D. 7.5 𝑚