Question

The angle of elevation of the top of a tower from a point on the horizontal ground, 40m away from the tower is 30°, Find the height of the tower.

Answer 1

Answer:

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

Now in ΔABC:

tan30°=BC/AB

1/√3 =h/40 (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)mtrs

Then the height of tower =40√3 mtrs,

and the depth up tank is 40(1-1√3).