Question

A boy sees the top of a tower with an angle of elevation 60 degree. stepping 20m back he sees the top with angle of elevation 30 degree. Calculate the height of the tower.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

height of the tower is 10√3 m

Step-by-step explanation:

let 'h' be the height of the tower

'x' be the distance from ground level when angle of elevation is 60 degree.

'x+20' be the distance from ground level when angle of elevation is 30 degree

refer to the image attached

in triangle ABC,

tan 60 = $\frac{h}{x}$

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

x = $\frac{h}{\sqrt{3} }$  ______ eq(1)

in triangle ABD

tan 30 = $\frac{h}{x+20}$

$\frac{1}{\sqrt{3} } =$ $\frac{h}{x+20}$

x+20 = √3h

x = √3h - 20 ______eq(2)

compare eq (1) & (2)

$\frac{h}{\sqrt{3} }$ = √3h - 20

h= 3h - 20√3

2h = 20√3

h = 10√3 m

therefore, height of the tower is 10√3 m