SOLUTION: From an airplane at an altitude of 1200 m, the angle of depression to a building on the ground measures 28 degrees. What is the distance from the plane to the building?

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Question 1150825: From an airplane at an altitude of 1200 m, the angle of depression to a building on the ground measures 28 degrees. What is the distance from the plane to the building?
Found 2 solutions by 4419875, MathTherapy:
Answer by 4419875(21) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem, by analysis, we can form a right triangle and by this reason, the
altitude shall be the height and the distance of the building, at a given angle, to the airplane is the hypotenuse. With the given parameters, we can apply the trig function of sine, wherein sin%28x%29=opposite%2Fhypotenuse
Now by plugging in the values
sin%2828%29=1200m%2Fh
h=1200m%2Fsin%2828%29
where h=2556.065m

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

From an airplane at an altitude of 1200 m, the angle of depression to a building on the ground measures 28 degrees. What is the distance from the plane to the building?
The distance from the plane to the building is actually the same as the distance from the building to the point on the GROUND, directly below the plane. Therefore, with a right-triangle

being formed, with the side opposite the 28o∡ being 1,200 m, and the unknown adjacent side (D) being sought, we get the following trigonometric function: 

Solve this for D, the distance from the plane to the building!

Note that the 28o∡ of depression is from the plane to the BASE/BOTTOM of the building, and not the TOP.