An airplane is flying at an elevation of $150 ft, directly above a straight high

Question

An airplane is flying at an elevation of $150 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane. The angle of depression to one car is 33 degree, and that to the other is 54 degree. How far apart are the cars? (Round your answer to the nearest foot.) To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75 degree from the horizontal. An observer D = 500 m away measures elevation to the spot of light to be 45 degree. Find the height h of the cloud cover. (Round your answer to the nearest meter)

Explanation / Answer

Let x ft be the distance of one motorist and y be the distance of another motorist

According to question

tan 33=5150/x   and tan 54=5150/y

x=5150/tan 33    and   y= 5150/tan 54

x= 7930.3 feet   and y= 3741.69 feet

Therefore distance between the two motorist= x+y=11672 feet

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