1. Angles of Elevation / Depression
OBJ: Solve problems involving angles of elevation/depression

2. Angle of Elevation Angle of DepressionY X X Y

3. EX: Donna Spence know that when she stands123 ft from the base of a flag pole, the angle of elevation to the top is 26º 40´. If her eyes are 5.30 ft above the ground, find the height of the flag pole. x
26.7
Donna
123
tan (26.7) = x
123 tan (26.7) = x
61.9 = x
= 67.2 feet = height of the flagpole

4. sun y 55º 210 tan(55) = y 210 tan(55) = y = 300ft
EX: The tallest flagpole in the world was built in San Francisco in When the angle of elevation of the sun was 55º, the length of the shadow cast by the flagpole was 210 ft. Find the height of the flagpole (to the nearest foot)
sun y
55º
210
tan(55) = y
210 tan(55) = y
= 300ft

5. sun 300 34º x tan(34) = 300 300/tan(34) = x = 445 ft
EX: What was the length of the shadow when the angle of elevation of the sun was 34º?
sun
300
34º x
tan(34) = 300
300/tan(34) = x
= 445 ft

6. 3000 trees 19.5 tan(19.5º) = 3000 |X| x x = 3000 tan(19.5º)
EX: From a hot-air balloon 3000ft above the ground, you see a clearing whose angle of depression is 19.5º. What is your horizontal distance from the clearing? Round to the nearest foot.
Balloon x
trees
tan(19.5º) = |X| x
x = 3000
tan(19.5º)
= 8472 feet

7. EX: Park Planners would like to build a bridge across a creek
EX: Park Planners would like to build a bridge across a creek. Surveyors have determined that from 5 ft. above the ground the angle of elevation to the top of an 8 ft. pole on the opposite side of the creek is 5º. Find the length of the bridge to the nearest foot. 5º 5 x
tan 5º = 3
x = 3/ tan 5º = 34.3 ft

8. EX: Now suppose the bridge will be 12 in. above ground level
EX: Now suppose the bridge will be 12 in. above ground level. A 10 ft ramp will be built between the ground and the bridge. What angle will the ramp make with the ground? ( to the nearest tenth of a degree)
10ft
1ft
(12in)
sin  = 1 10
sin-1 (1/10) =
5.7º