This document discusses angles of elevation and depression. It defines an angle of elevation as the angle formed between a horizontal line and the line of sight to an object located above the horizontal line. An angle of depression is defined as the angle formed between a horizontal line and the line of sight to an object located below the horizontal line. The document provides examples of solving problems involving angles of elevation and depression using trigonometric functions like tangent, sine, and the Pythagorean theorem. It emphasizes drawing a diagram, identifying if it is an angle of elevation or depression, and using the appropriate trigonometric ratio to solve for missing lengths.

1. Angle of Elevation and
Depression
Prepared By:
Bebe-Ann Buar

2. Objectives:
1. Distinguish the difference between angle of elevation and
depression.
2. Solve problems involving angles of elevation and depression.
3. Identify the relationship between an angle of elevation and
depression in a right triangle.
4. Appreciate the importance of angles of elevation and depression in
solving problems in real life situation.
At the end of this lesson, student will be able to:

3. ANGLE OF ELEVATION
⇛The angle of elevation is the angle formed by a horizontal line and the line of
sight up to an object when the image of an object is located above the
horizontal line.
⇛On the SAT, this is called angle of inclination.

4. ANGLE OF DEPRESSION
⇛The angle of depression is the angle formed by a horizontal line and the line
of sight down to an object when the image of an object is located beneath the
horizontal line.
⇛On the SAT, this is called angle of declination.

5. Angle of elevation and depression:

6. Angle of elevation and depression:

7. Angle of elevation and depression:

8. “Angle of elevation and depression must have one horizontal side”

9. “Angle of elevation and depression must have one horizontal side”
∠ACB is an Angle of
Elevation.
∠DBC is an Angle of
Depression.
∠ABC is NOT an angle
of Depression!!

10. NAMING ANGLE OF ELEVATION AND DEPRESSION
1
5
2
3
4
6
Angle of Depression
Angle of Elevation
Angle of Depression
Angle of Elevation
NOT AN ANGLE OF DEPRESSION
NOTE:
*Angle of elevation and depression always have a horizontal line and line of sight
(diagonal line).
*To identify whether an angle is an angle of elevation and depression, check whether
the line of sight is above or below the horizontal line.

11. ALTERNATE ANGLE
Alternate
angles are
always
congruent

12. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION

13. How To Solve Word Problems That Involve Angle
Of Elevation Or Depression?
STEPS TO FOLLOW:
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO

14. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
1. An observer standing on the top of a vertical
cliff spots a house in the adjacent valley at an
angle of depression of 12°. The cliff is 60m tall.
How far is the house from the base of the cliff?
12°
60 m
x
Angle of Depression
12°
78°
TOA
𝒕𝒂𝒏𝟏𝟐 =
𝟔𝟎
𝒙
𝒕𝒂𝒏𝟏𝟐( 𝒙)
𝒕𝒂𝒏𝟏𝟐
=
𝟔𝟎
𝒕𝒂𝒏𝟏𝟐
𝒙 = 𝟐𝟖𝟐𝒎

15. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
TOA
𝒕𝒂𝒏𝟓𝟎 =
𝒙
𝟖𝟕
𝒙 = 𝒕𝒂𝒏𝟓𝟎 𝟖𝟕
𝒙 = 𝟏. 𝟏𝟗𝟏𝟕 𝟖𝟕
𝒙 = 𝟏𝟎𝟑. 𝟕 𝒇𝒕.
2.

16. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
3.A home owner is to construct a ramp to his front door to
make it wheelchair accessible. How long is the ramp if the door
is 4ft above the ground level and the angle of elevation is 20°?
4ft
20°
x
SOH
𝒔𝒊𝒏𝟐𝟎° =
𝟒
𝒙
𝒔𝒊𝒏𝟐𝟎° (𝒙)
𝐬𝐢𝐧 𝟐𝟎°
=
𝟒
𝒔𝒊𝒏𝟐𝟎°
𝒙 = 𝟏𝟏. 𝟕𝒇𝒕

17. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
4. The height of an outdoor basketball backboard is 150
inch, and the backboard casts a shadow 208 inch long.
Find the angle of elevation
150 inch
208 inch
𝜃
𝒕𝒂𝒏𝜽 =
𝟏𝟓𝟎
𝟐𝟎𝟖
𝜽 = 𝒕𝒂𝒏−𝟏
𝟏𝟓𝟎
𝟐𝟎𝟖
𝜽 = 𝟑𝟓. 𝟖𝟎°
TOA

18. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
5. For a laser lightshow at an amusement park, the laser
beam directed from the top of a 30ft. building to reflect an
object that is 100ft. away from a point directly below the
location of the laser. What is the angle of depression from
the laser to the reflecting object?
30 ft
100 ft
TOA
𝒕𝒂𝒏𝜽 =
𝟑𝟎
𝟏𝟎𝟎
𝜽 = 𝒕𝒂𝒏−𝟏
𝟑𝟎
𝟏𝟎𝟎
𝒙 = 𝟏𝟔. 𝟕°
𝜃

19. When do we apply the
Pythagorean Theorem in solving
problems involving angles of
elevation and depression?

20. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
1.A home owner is to construct a ramp to his front door to
make it wheelchair accessible. How long is the ramp if the door
is 4ft above the ground level and the angle of elevation is 20°?
4ft
20°
x
SOH
𝒔𝒊𝒏𝟐𝟎° =
𝟒
𝒙
𝒔𝒊𝒏𝟐𝟎° (𝒙)
𝐬𝐢𝐧 𝟐𝟎°
=
𝟒
𝒔𝒊𝒏𝟐𝟎°
𝒙 = 𝟏𝟏. 𝟕𝒇𝒕
Find the ground level measurement.
𝑎2
+ 𝑏2
= 𝑐2
42
+ 𝑏2
= 11.72
16 + 𝑏2
= 11.72
𝑏2 = 136.89 − 16
𝑏2
= 120.89
𝑏 = 10.99

21. SOLVING PROBLEMS INVOLVING ANGLES OF
ELEVATION AND DEPRESSION
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or
depression.
Step 3: Use trigonometry to find the required
missing length.
SOH, CAH, TOA, CHO, SHA, CAO
2. An observer standing on the top of a vertical
cliff spots a house in the adjacent valley at an
angle of depression of 12°. The cliff is 60m tall.
How far is the house from the base of the cliff?
12°
60 m
x
Angle of Depression
12°
78°
TOA
𝒕𝒂𝒏𝟏𝟐 =
𝟔𝟎
𝒙
𝒕𝒂𝒏𝟏𝟐( 𝒙)
𝒕𝒂𝒏𝟏𝟐( 𝒙)
=
𝟔𝟎
𝒕𝒂𝒏𝟏𝟐
𝒙 = 𝟐𝟖𝟐𝒎
Find the measurement of the line of sight down to the object.
𝑎2
+ 𝑏2
= 𝑐2
62 + 2822 = 𝑐2
𝑐2 = 83124
𝑐 = 288.31

22. That’s all!
I hope you’ve learn something from me!