Question

the shadow of a vertical tower on level ground increases by 10m when the altitude of the sun changes from 45° to 30°. find the height of the tower

Answer 1

Answer:

Step-by-step explanation:

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