Angles of Elevation / Depression

OBJ: Solve problems involving angles of elevation/depression

Angle of Elevation Angle of Depression

Y

X X

Y

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 5.3

123

tan (26.7) = x

123

123 tan (26.7) = x

61.9 = x

61.9 + 5.3 = 67.2 feet = height of the flagpole

EX: The tallest flagpole in the world was built in San Francisco in 1915. 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 210210 tan(55) = y = 300ft

EX: What was the length of the shadow when the angle of elevation of the sun was 34º?

sun

300

34º

xtan(34) = 300 x300/tan(34) = x = 445 ft

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 19.5

3000 trees 19.5

tan(19.5º) = 3000 |X|

x

x = 3000

tan(19.5º)

= 8472 feet

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 8

5

xtan 5º = 3 xx = 3/ tan 5º = 34.3 ft

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)

10ft1ft(12in)

sin = 1 10sin-1 (1/10) =5.7º