A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 35°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 39°. At that time, what is the distance between him and his friend

Question

Mathematics

Aarav Pope

8 June, 23:35

A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 35°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 39°. At that time, what is the distance between him and his friend

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Answers (1)

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Dexter Shah · Answer 1

322.21 feet

Step-by-step explanation:

Flying rate = 6 ft/s

Angle of depression from his balloon to a friend's car = 35 °

One and half minutes later, he observed the angle of depression to be 39°

Time = 1 mins 1/2 seconds

= 3/2 mins

= 3/2 * 60

= 3*30

= 90 secs

Speed = distance / time

Distance = speed * time

= 6*90

= 540 ft

The angle on the ground = 180° - 35° - 39°

= 180° - 74°

= 106°

Let the distance between him and his friend be x

Using sine rule

x/sin 35 = 540/sin 106

x = (540sin 35) / sin 106

x = 322.21ft