Top Fountains

UCLA Inverted Fountain

A very exciting short video of UCLA's Inverted Fountain, located in South Campus. It was completed in 1968 with a recirculating water flow of 10000 gallons per minute and was inspired by the bubbling mud pots and natural hot springs (Morning Glory Pool) in Yellowstone National Park.

Question by Countrygurl: How do I find the height of a fountain in the center of a circular pool?
A high fountain of water is located at the
center of a circular pool. A
student walks around the pool and estimates
its circumference to be 63.2 m. Next, the
student stands at the edge of the pool and uses
a protractor to gauge the angle of elevation of
the top of the fountain to be 45.4◦.
How high is the fountain? Answer in units
of m.

I have used a formula of tan( 45.4 = x/10.06 (with 10.06 being the radius)
Then, i multiplied each side by 10.06, leaving, 10.06 (tan( 45.4)) = X

X= 65.2 m

I can think of no other way to do this, and all of the answers that I've given have been wrong. HELP!!!

Best answer:

Answer by Joshua
Here I am to save you. : )

Let's start off with what we know. There is a fountain in the center of a circular pool that has a height of unknown length. Take a picture of that from a side point of view.

We can draw it to look something like this:

__|__

I know, a bad drawing with ascii, but it works. As we can see we could creat a triangle by connecting the top of the fountain to the side of the pool.

Now let's mark our angles. We know the obvious angle in the bottom middle is 90 degrees. It is given in our facts that the angle at the top is 45.4 degrees. Thus by elimination, our last angle must be 44.6 degrees.

Next, let's figure out the side (i.e. the radius). The circumference of a circle is diameter * Pi. Solve for the diameter and you get 10.06 just like surmised.

We now have all of the information we need.

Let's take a look at the lower left angle in the diagram I explained above. That angle, as we figured out through simple arithmetic, is 44.6 degrees. We know that a tan of an angle is the Opposite Side divided by the Adjacent Side.

Thus, the tan(44.6) would be the unknown height of the fountain (we'll call it "x") divided by the radius that we just figured out (10.06). Thus your formula looks like this:

tan(44.6 degrees) = x / 10.06

Multiply by 10.06 on both sides to get x alone:

10.06 * tan(44.6) = x

My solution was x = 9.9

Make sure your calculator is in Degree Mode as well. I hope I helped. : )

EDIT: I just realized that the given angle you were talking about was the angle from the BOTTOM to the TOP. I misread that. However, it is a very slight change in calculation. Simply change the tangent I have in my formula to 45.4, and your new answer will be:

x = 10.2

: ) Again, check for Degree Mode!

Know better? Leave your own answer in the comments!

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