Question

An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 34° and to the other is 54°. How far apart are the cars? (Round your answer to the nearest foot.)

Answer 1

The cars are 10702ft apart

Explanation:

Height of the plane from the high way = 5150ft

Considering Triangle ABD, we will be using SOHCAHTOA

Tan = Opposite/ Adjacent

Tan 54° = Y/5150

Y = 5150*tan54°

Y = 7088 ft

Considering Triangle ADC, Tan = Opposite/ Adjacent is also applicable

Tan 34° = X/5150

X = 5150*tan 54°

X = 3614ft

The distance between the two cars = (X+Y)

= 7088 + 3614

= 10702ft