SOLUTION: From the edge of a 1000 ft. cliff, the angles of depression to two cars in the valley below are 21� and 28�. How far apart are the cars? Round your answers to the nearest 0.1 ft.

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Question 192724: From the edge of a 1000 ft. cliff, the angles of depression to two cars in the valley below are 21� and 28�. How far apart are the cars? Round your answers to the nearest 0.1 ft.
Found 2 solutions by RAY100, jojo14344:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
the angle of depression means the angle between a horizontal line and the sight line.
In this case the sight line is from the top of the cliff to the car position.
The triangle formed would be a right triangle, the hypotenuse the sight line, the vertical leg the height of the cliff, and the horizontal leg the distance from the cliff.
in one instance the angle of 28 degrees is between the sight line and the horizontal line representing the ground. The trig function tan would = height of the cliff divided by the horizontal distance from cliff.
tan 28 = 1000/x
x= 1000/ tan 28 =1880.726
likewise the other case finds tan 21= 1000/y, y=1000/tan21=2605.089
the difference in distance from cliff = 2605.089-1880.726 = 724.363 =724.4

Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website!

Okay, let us see the cars with the Angle of Depression on the cliff:

By Trigo Function:

Also,

Therefore, the distance between cars:

, Answer

Thank you,
Jojo