Question

The length of the shadow of a statue increases by 8m, when the latitude of the sun changes from 45° to 30°. Calculate the height of the tower. 

Answer 1

Let the height of the statue (AB) be h. 

In ΔABC,

`tan45^circ = "AB"/"BC"`

⇒ BC = h

In ΔABD,

`tan30^circ = "AB"/"BD"`

`1/sqrt(3) = "AB"/("BC + CD")`

h + 8 = `sqrt(3)`h    (∵ BC = h)

⇒ `"h"(sqrt(3)` - 1) = 8

⇒ h = `8/(sqrt(3) - 1) × (sqrt(3) + 1)/(sqrt(3) + 1)`

⇒ h = `(8(sqrt(3) + 1))/2 = 4(sqrt(3) + 1) = 4 xx 2.732 = 10.928 ≈ 10.93`

Thus, the height of the tower is 10. 93 m.