Question

The shadow 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 the tower , correct to two decimal places.

Answer 1

Answ

The shadow of a vertical tower on level ground increase by 10 m when the altitude of sun changes from angle of elevation 45 to30 find the height of tower

Ask for details Follow Report by Astha42 31.12.2017

Answers

ashishkhare687

ashishkhare687 Ace

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