SOLUTION: Two tanks on a training mission are 1,800 m apart on a straight road. The drivers find the angles of elevation to the helicopter hovering over the road between them to be 33° and 5

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Question 308244: Two tanks on a training mission are 1,800 m apart on a straight road. The drivers find the angles of elevation to the helicopter hovering over the road between them to be 33° and 52°. Find the height of the helicopter to two significant digits.
Answer by mananth(16949) About Me  (Show Source):
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Two tanks on a training mission are 1,800 m apart on a straight road. The drivers find the angles of elevation to the helicopter hovering over the road between them to be 33° and 52°. Find the height of the helicopter to two significant digits.
Let point from where the angle observed as 33deg be A
Let point from where the angle observed as 52deg be B
The point of intersection of the vertical from the helicopter to the ground be C
.
AB is given as 1800 meters
Let BC be x meters
ABC form a right triangle
Tan 33 = vertical height / x+1800
vertical height = tan33 * (x+1800)
.
.
Tan 52 = vertical height / x
x*tan 52 = vertical height
So
xTan 52 = Tan 33* ( x+1800)
1.2799x = 0.6494(x+1800)
1.2799x= 0.6494x +1168.92
0.6305x= 1168.92
x= 1854 meters
1800+1854 = total distance from point A
=3654 meters
Tan 33= vertical height / 3654
vertical distance= 3654*tan33
= 2372.90 meters