A high fountain of water is located at the center of a circular pool as in Figure P1.41. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 39.0 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?
By knowing the circumference (P) of the pool one can compute its radius (r)
$r =P/(2\pi) =39/(2*3.14) =6.21 m$
Let h be the height of the fountain. In the right triangle formed by the radius r with the height h one has
$h =r*tan(55) =6.21*tan(55) =8.87 m$