Use trig to solve problems

1. Trig Applications
The student is able to (I can):
• Solve problems using trigonometry
• 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 aboveaboveaboveabove the line.
angle
This is also sometimes 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 belowbelowbelowbelow the line.
angle
This is also sometimes 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 2. ∠2
3. ∠3 4. ∠4

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

7. 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?
35˚
18´ (adj)
x
(opp)

8. 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?
35˚
18´ (adj)
x
(opp)
tan35
18
18tan35
13 feet
x
x
x
° =
= °
=

9. 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´
(27˚)
x

10. 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
3000
5888 feet
tan27
x
x
° =
= =
°