Question

The shawdow of a vertical tower on a level ground increases by 10m when the altitude of the sun changes from 45 to 30 find the height of a tower correct to two decimal places

Answer 1

as the shadow increase by 10 m
let the total distance when the sun elevation was 45 is x
whereas when the sun elevation was 30 the distance increased by 10 m so x + 10 

let h be the height of tower
when the sun elevation was 45 
tan 45 = h/x
1 = h/x
x = h .............(i)
 
when the sun elevation was 30
tan 30 = h / (x +10)
1/√3 = h / (x + 10)
(x + 10) / √3 = h..................(ii)

from (i) and (ii) we get
x = (x + 10) / √3
√3x = x + 10
√3 x - x = 10
x( √3 - 1) = 10
x = 10 / ( √3 - 1)
x = 10 / ( √3 - 1) * ( √3 +1) / ( √3 +1) ................ rationalising the denominator
x = 10 ( √3 +1)/ (√3)² - (1)²
x = 10 ( √3 +1) /3 -1
x = 10 ( √3 +1) /2
x = 5 ( √3 +1) 
from (i) we get
x = h
5 ( √3 +1)  m = height of tower