SOLUTION: 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 mark

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Question 1169495: 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 38°. 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? (Round to the nearest foot.)
Answers I have gotten so far that are incorrect: (283,284,285,268,269,270) I am lost. Any help is appreciated!!!!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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 38°.
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?
:
Find the distance the balloon travels in 1.5 min which is the distance between the two observations made to the car.
1.5 * 60 * 6 = 540 ft.
This forms a triangle, the two points and the car, angles 38 and 39, we can find the 3rd angle 180 - 38 - 39 = 103 degrees.
this is the angle at the car with the two observation points
Let d = the distance from the car after passing over it
Use the law of sines:
=
cross multiply
sin(103)*d = sin(38)*540
.97347d = 332.46
d =
d = 341.2 ft to the car