Question

A flagstaff stands on a vertical pole. The angles of elevation of the top and the bottom of the flagstaff from a point on the ground are found to be 60° and 30° respectively. If the height of the pole is 2.5m. Find the height of the flagstaff. 

Answer 1

Let AB be the flagstaff, BC be the pole and D be the point on ground from where elevation angles are measured. 

In ΔBCD 

`"BC"/"CD" = tan 30^circ`

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

`sqrt(3)"BC" = "CD"`   ....(1)

In ΔACD

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

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

`"AB" + 2.5 = "CD"sqrt(3) = 3"BC"`  [Using (1)]

`"AB" + 2.5 = 3 xx 2.5`

`"AB" + 2.5 = 7.5`

AB = 5

Thus , the height of the flagstaff is 5 m.