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?

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

Amswer:

the fountain is 43.19 m high