Question

The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. Find the height of the tower, correct to two decimal places.

Answer 1

Let the height of tower be h meter and length of shawdow y meter initially.

In ΔABC,
tan 45° = `"AB"/"BC"`

1 = `h/y`

y = h     ...(1)

In ΔABD,
tan 30° = `"AB"/"DB"`

`1/sqrt3 = h/(y + 10)`

y + 10 = h`sqrt3`    ...(2)

Put y = h in equation (ii),

h + 10 = `hsqrt3`

`h(sqrt3 - 1) = 10`

h = `10(sqrt3 + 1)/((sqrt3 - 1)(sqrt3 + 1))`

h = `10/(3 - 1) (sqrt3 + 1)`

h = `10/2(sqrt3 + 1)`

h = 5(1.732 + 1)

h = 5 × 2.732 

h = 13.66 meter