Question

A high fountain of water is located at the center of a circular pool as shown in the figure below. A student walks around the pool and measures its circumference to be 15.6 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation of the top of the fountain to be ϕ = 54.0°. How high is the fountain?

Answer 1

Let point O be the centre of circular pool, point A be the top of the fountain and point B be the edge of the pool.

Circumference of circle=$15.6m=2\times 3.14\times radius$

Now,

$radius=2.484m$ $=$ OB

In$\triangle OAB$

$\cos(54\degree)=0.5877=\frac{OB}{AB}$

AB$=\frac{OB}{0.5877}=\frac{2.484}{0.5877}=4.226$

$\sin(54\degree)=0.8090=\frac{OA}{AB}$

$OA=0.8090\times AB=0.8090\times 4.226=3.42m$

So, Height of fountain $=3.42m$