1. Angle of Elevation & Angle of Depression

2. When a person looks at something above his/her location, the angle between the line of sight and the horizontal is called the angle of elevation. In this case, the line of sight is "elevated" above the horizontal.
Object
Eye

3. When a person looks at something below his or her location, the angle between the line of sight and the horizontal is called the angle of depression. In this case, the line of sight is "depressed" below the horizontal.
Eye
Object

4. A stands at the window of a
so that his are 12.6 m above the
level ground in the vicinity of the
An object is 58.5 m away from the
on a line directly beneath the
Find the angle of depression of the
person's line of sight to the object on the
ground.

5. Solutions  = angle of depression   12.15º  eye Line of sight 12.6m
Ground level
object
58.5m

6. Exercise Calculate the angle of elevation of the
line of sight of a person whose eye is
1.7 m above the ground, and is looking
at the top of a tree which is 27.5 m away
on level ground and 18.6 m high.

7. Sketch

8. Solution
  31.57º
Angle of elevation of this person line of sight is 31.57º

9. Angle of depression Find the height of the man in the
hot air balloon from the ground.
= 50°
h =100 tan 50°
= 119.2m h
100m

10. FIND THE HEIGHT OF THE TOWER
Exercise
FIND THE HEIGHT OF THE TOWER
Height of tower
= 53 tan 80°
= 300.6m
80º
53m

11. Exercise From the top of a vertical cliff 40 m high,
the angle of depression of an object
that is level with the base of the cliff is
34º. 
How far is the object from the base of
the cliff?

12. Solution Let x m be the distance of the object
from the base of the cliff.

14. Percent Grade
When talking about the slope of a road, it is usually called the road grade. Grade is commonly expressed as a percentage.
Grade – the slope of a physical feature such as a road or hill, often expressed as a percentage.
Percent grade = rise/run x 100

15. Percent Grade Example
Martin is driving his truck on the highway. There is a sign indicating a 7% grade.
What is the slope of the road, as a fraction?
Find the angle of elevation of the road.
Percent grade = rise /run x 100
7% = rise/run x 100
7/100 = rise/ run
The slope of the road is 7/100 or .07