Question

A vertical pole of 30 m is fixed on a tower. From a point on the level ground, the angle of elevation of the top and bottom of the pole is 60° and 45°. Find the height of the tower.

Options

• 20

• `15 (sqrt3 + 1)`

• `15 (sqrt3 - 1)`

• 15

Answer 1

`15 (sqrt3 + 1)`

Explanation:

The situation can be represented by the figure above

`"tan"  60^circ = "AC"/"CD" = ("AB" + "BC")/"CD"`

`=> ("CD") "tan"  60^circ = "AB" + "BC"`.....(1)

`"tan"  45^circ = "BC"/"CD"`

`=> ("CD") "tan"  45^circ = "BC"`.....(2)

Dividing eq (1) by (2)

`("tan"  60^circ)/("tan"  45^circ) = ("AB" + "BC")/"BC"`

`=> "BC" = "AB"/((sqrt3 - 1)) = 15 (sqrt3 + 1) "m"`