Question

A vertical tow er stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the ft agstaff is 45°. Find the height of the tower. 

Answer 1

Let AB be the flagstaff, BC be the tower 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"`

In ΔACD

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

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

`7 + "BC" = sqrt(3)"BC"`

`"BC"(sqrt(3)-1) = 7`

BC = `((7)(sqrt(3) + 1))/((sqrt(3) - 1)(sqrt(3) + 1)`

= `(7(sqrt(3)+ 1))/((sqrt(3))^2 - (1)^2)`

= `(7(sqrt(3) + 1))/2 = 3.5(sqrt(3) + 1) = 3.5 xx 2.732 = 9.562`

Thus , the height of the tower is 9.562 m = 9.56 m.