Question

A student walks around a pool and estimates the pool has a circumference of 240 m.
Using a protractor the students gages the angle of elevation to the top of the fountain, in the center of the pool, to be 74 degrees.

Answer 1

This question in incomplete. Do they want to know the height of the fountain?

That would be H = R*tan74, where

R = 240/(2 pi) = 38.2 meters.

Now compute H.

It seems rather high to me.

Answer 2

Oh, yes. I am sorry.
I am attempting to calculate the height of the fountain.

It does indeed seem rather high. But the numbers for my assignment are randomly generated. So that may explain this phenomenon.
Thank you for your help.

Answer 3

So what is your question? I'm assuming
you want to know the height of the fountain.

C = 6.28r = 250m,
r = 250 / 6.28 = 39.8m.

tan74 = h/r = h / 39.8
h = 39.8tan74 = 138.8m.

Answer 4

drwls, you finished a little ahead of me: but that's good because i used the wrong value for the circumference.