Question

When the length of shadow of a vertical pole is equal to `sqrt3` times its height, the angle of elevation of the Sun’s altitude is ____________.

Options

• 30°

• 45°

• 60°

• 15°

Answer 1

When the length of the shadow of a vertical pole is equal to `sqrt3` times its height, the angle of elevation of the Sun’s altitude is 30°.

Explanation:

Let the height of the vertical pole, BC = hm
`therefore "Shadow AB" = sqrt3  "hm and the angle of elevation ZBAC" = theta`

In rt `angle "ABC, tan"  theta  "BC"/"AB" = "h"/(sqrt3 "h") = 1/sqrt3 = "tan"  30^circ`

`therefore theta = 30^circ`

Hence the Sun’s altitude is 30°