Question

From a point on the ground 40m away from the foot of tower, the angle of elevation of the top of the tower is 300. The angle of elevation of the top of a water tank ( on the top of tower) is 450. Find the height and the depth of the tank.

Answer 1

Hello,

let h  m be the height of tower and  m be the depth of tank (as figure).

Now, in ΔABC:

tan30°=BC/AB;

1/√3=h/40;

h=40/√3 m     (1)

 In ΔABD:

tan45°=DC+BC/AB;

1=x+h/40;

x+h=40;

using (1):

x+40/√3=40;

x=40(1-1/√3) m

Then height of the tower = 40/√3 m,

and depth up tank :

40(1-1/√3)m

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Answer 2

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