I do acknowledge those references, sites, and pictures that I use to have this ppt.

1. Activity 1: Look Up! Look Down!
Follow the steps below and answer the
that follow.
 Ask for your member to stand and using
measure or ruler determine his height
 Look around the room for an object which
have the same height with your member
 Determine the distance between your
and the object

2. Describe the illustration or
picture you have created from
the activity.
1. What mathematical concepts
did you learn from the activity?

3. Angles of Elevation and
Angles of Depression

4. 2. When you look up to
tall objects is there an
angle formed? What
about when you look
down?

5. 3. Do you think you can directly
measure the height, the distance of
the object you have listed in the
activity

7. Illustrative Example
A hiker is 400 meters away from
the base of the radio tower. The
angle of elevation to the top of
the tower is 46°. How high is
the tower?

8. Step 1: Draw a sketch of the
situation.
Step 2: Mark in the given
angle of elevation or
depression

10. From the given
illustration what
trigonometric function
to be use?

11. SOH? CAH?
TOA?

12. SOH? CAH?
TOA?

13. Step 3: Use trigonometry to find
the required missing length
Solution: 𝑇𝑎𝑛 46° =
𝑜𝑝𝑝
400
𝑜𝑝𝑝 = 400𝑡𝑎𝑛46°
414.21 𝑚

14. no. 2 (angle of elevation)
A man who is 2 m tall stands on
horizontal ground 30 m from a
tree. The angle of elevation of
the top of the tree from his eyes
is 28˚. Estimate the height of the

15. Step 1: Draw a sketch of the
situation.
Step 2: Mark in the given angle of
elevation or depression.
Let the height of the tree be h.
Sketch a diagram to represent the
situation

17. SOH? CAH?
TOA?

18. Step 3: Use trigonometry to find the
required missing length
𝑡𝑎𝑛 28° =
ℎ−2
30
ℎ − 2 = 30 tan 28°
ℎ = 30 × 0.5317 + 2 ← tan 28° = 0.5317
ℎ = 17.951
The height of the tree is approximately
17.95 m.

19. a. What is/are difference
between angle of elevation and
angle of depression?

20. b. How to solve problems
involving angles of elevation
and depression?

21. Groupings

22. 1.A girl is sitting in the shade under a tree that is
90 ft from the base of a tower. The angle of
elevation from the girl to the top of the tower is
35 degrees. Find the height of the windmill.
2.The angle of depression of a stone on the
ground from the top of a tower is 45°. If the
stone is at a distance of 120 meters away from
the building, find the height of the tower.

23. 3. From two points 100 ft apart in a straight line to
the base of a tree, the angle of elevation to the top
of the tree are 38° and 53° respectively. Find the
height of the tree.
4.An observer in a lighthouse 48.8 m above sea level
saw two vessels moving directly towards the
lighthouse. He observed that the angles of
depression are 42° and 35°. Find the distance
between the two vessels, assuming that they are
coming from the same side of the tower.

24. Things to Remember
The angle of elevation is the angle
between the imaginary line of sight and
horizontal line, where the object is above
the observer.
The angle of depression is the angle
between the imaginary line of sight and a
horizontal line, where the object is below
the observer.

25.  A trigonometric ratio often helps us set
up an equation, which can then be solved
for the missing measurement. If two legs
of the triangle are part of the problem,
then it is a tangent ratio. If the
hypotenuse is part of the problem, then it
is either a sine or cosine ratio.

27. a. Find the height of a hot air balloon

28. b. Find the measure of angle x above the ground.