Question

From a point on the level ground , the angle of elevation of the top of a pole is 30 degrees. On moving 20mts nearer,the angle of elevation is 45 degrees. Then the height of the pole in mts is

Answer 1

Step-by-step explanation:

let the height of the tower be h and the distance of the point from the foot of the tower be x

then h/x= tan(30°)

->

$\frac{h}{x} = \frac{1}{ \sqrt{3} }$

—---———————————(1)

$x = \sqrt{3} h$

when moving 20m nearer the distance from the foot of the tower is x-20

$\frac{h}{x - 20} = \tan(45) = 1$

h=x-20

x=h+20 ———————————(2)

from (2)

$h + 20 = \sqrt{3} h$

$h = \frac{20}{ \sqrt{3} - 1 }$

$h = 10( \sqrt{3} + 1)$

h=27.32