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

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) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
A recent poll by the American Automobile Club found that 78.2% of those surveyed are... (answered by Boreal)

Two boats, 70 meters apart and on the opposite sides of a light house, are in a straight... (answered by josgarithmetic)

Two cross-country skiers come to a fork on the road. They then split up one to each... (answered by ikleyn)

A recent poll found that 42% of those surveyed are worried about aggressive drivers on... (answered by Fombitz)

Suppose that you are at the base of a hill and see a sign that reads "Elevation 3700... (answered by josgarithmetic)

Two houses on the same road are 10 miles apart. The angles formed between the road and... (answered by ankor@dixie-net.com)

A hot air balloon is floating above a straight road. To estimate their height above the... (answered by mananth)

Two boys are on opposite sides of a tower.They sight the top of the tower at 33 degree's... (answered by ankor@dixie-net.com)

Bob is driving along a straight and level road straight toward a mountain. At some point (answered by mananth)