Question

A fountain of water is located at the center of a circular pool. Not wishing 

to get his feet wet, a student walks around the pool and measures its 

circumference to be 16.5 m. Next, the student stands at the edge of the pool 

and uses a protractor to gauge the angle of elevation at the bottom of the 

fountain to be 55.0°. How high is the fountain?

Answer 1

Since the circumference is $L = 16.5 m$, the radius of the pool is:

$$r = \dfrac{L}{2\pi}$$

From the right triangle in which one leg is radus, and another leg is the fountain, the height of the fountain is:

$$h = r\tan\theta = \dfrac{L\tan\theta}{2\pi}$$

where $\theta = 55\degree$ is the angle measured by the student. Thus, obtain:

$$h =\dfrac{16.5\cdot \tan55\degree}{2\pi} \approx 3.75m$$

Answer. 3.75m.