Question

A vertical tower stands on a horizontal plane and is surmounted by a flag-staff of height 7 m. From a point on the plane, the angle of elevation of the bottom of the flag-staff is 30° and that of the top of the flag-staff is 45°. Find the height of the tower.

Answer 1

Height of the tower = (√3-1)/7 m

Step-by-step explanation:

The tower and flagstaff form the perpendicular of the right-angled triangle. Flagstaff is 7m in height. Let height of the tower be x. Let AB be the perpendicular, the opposite side to angle C. Angle B is 90 degrees. AC is the hypotenuse and BC is the adjacent side.

So Tan 30 = Opposite/adjacent

  1/√3 = x/BC

 So BC = x√3 ----(1)

 Now Tan 45 = opposite / adjacent

   1 = (7 + x) / BC

Substituting BC, we get:

 BC = 7 + x

 x√3 = 7 + x

 x = (√3-1)/7 m