SOLUTION: 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
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Question 429711: 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 35° and to the other is 57°. How far apart are the cars? Round your answer to the nearest foot. Answer by solver91311(24713) (Show Source):
Consider the triangle with vertices at the aircraft, the car with the angle of depression, and the point on the ground directly below the aircraft.
Given the angle of depression of , the angle of the triangle at the aircraft vertex must be the complement of the depression angle, namely
Let represent the distance from the point on the ground immediately below the aircraft and the car with the angle of depression.
Then
hence
Using your calculator you can easily calculate the value of
If you let represent the distance from the point on the ground immediately below the aircraft and the OTHER car, you can use the same process above to derive
The sum rounded to the nearest foot, is the desired distance.
John
My calculator said it, I believe it, that settles it
