A high fountain of water is in the center of a circular pool of water. you walk the circumference of the pool and measure it to be 190 meters. you then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. it is 55°. how high is the fountain?

Accepted Solution

The first thing we must take into account is that the circumference of the pool is given by:
 2 * pi * R = 190
 From here, we clear the radio:
 R = (190) / (2 * pi)
 R = 30.23943919 m
 Then, you can see the problem as a rectangle triangle, where the height of the source will be given by the following trigonometric relationship:
 tan (55) = H / R
 From here, we clear the height H:
 H = R * tan (55)
 H = (30.23943919) * tan (55)
 H = 43,1863948 m
 the fountain is 43.19 m high