Question

The length of the shadow of a tower standing on level ground is found to be 2x meters longer when the sun’s altitude is is 30° than when it was 45°. Prove that the height of the tower is x(root3 + 1) meters.

Answer 1

Solution-:

let height of tower = y
y/ y+ 2x= tan30
y/y+ 2x = 1/sqrt3
or y* sqrt3 = y + 2x
or y [ sqrt3 - 1] = 2x
or y = 2x/(sqrt3-1)
or y = 2x( sqrt3 + 1 )/ (sqrt3-1) (sqrt3 +1)
or y = 2x ( sqrt3 +1)/ 3 - 1
or y = 2x( sqrt 3+1 )/2
or height of tower = x*(sqrt3 +1) proved