Question

Mr.Hall stands 200 meters from the base of the water tower. He finds the angle of elevation to the top of the water to be 27 degrees. What is the hight of the tower?

Answer 1

Height of the tower = 101.9 m

Solution:

Given data:

Angle θ = 27°

Adjacent side = 200 m

Opposite side = Height

Let height be taken as h.

The given image shows it is a right triangle.

Using basic trigonometric ratio formulas,

`$\tan \theta=\frac{\text { Opposite side of } \theta}{\text { Adjacent side of } \theta}`

`$\tan27^\circ =\frac{{ h}}{200}`

The value of tan 27° = 0.5095

`$0.5095 =\frac{{ h}}{200}`

Do cross multiplication, we get

0.5095 × 200 = h

101.9 = h

Height of the tower = 101.9 m