Solve problems using angles of elevation and depression

1. Obj. 42 Elevation and Depression
The student is able to (I can):
• Solve problems involving angles of depression or elevation

2. angle of elevation
This is an angle formed by a horizontal
line and the line of sight to a point above
the line.
angle
On the SAT, this is called the angle of
inclination.

3. angle of depression
This is an angle formed by a horizontal
line and a line of sight to a point below
the line.
angle
On the SAT, this is called the angle of
declination.

4. These two angles are related because the
horizontal lines are parallel:
To identify whether an angle is an angle of
elevation or depression, check whether the
line of sight is above or below the horizontal
line.

5. Identify whether the angle is an angle of
elevation or depression.
1. ∠1
depression
2. ∠2
elevation
3. ∠3
depression
4. ∠4
elevation

6. Examples
1. If a tree casts a shadow 18 feet long
when the sun is at an elevation of 35˚,
how tall is the tree to the nearest foot?
x
(opp)
35˚
18‘ (adj)
x
tan35° =
18
x = 18 tan35°
x = 13 feet

7. 2. A plane, at an altitude of 3000 feet,
observes the airport at an angle of 27˚.
What is the horizontal distance between
the plane and the airport to the nearest
foot?
27˚
3000’
(opp)
(27˚)
x
(adj)
3000
tan27° =
x
3000
x=
tan27°
x = 5888 feet