Q&A: A high fountain of water is located at the center of a circular pool as in Figure P1.41. Not wishing to get hi
Question by jazzijazz101: A high fountain of water is located at the center of a circular pool as in Figure P1.41. Not wishing to get hi
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 25.0 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?
Best answer:
Answer by King Math
768.3 feet
Know better? Leave your own answer in the comments!
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March 26th, 2011 - 11:57
You can get the radius of the pool from the circumference which = 2*pi*r. Now you need to do some trig. Draw the fountain. Draw the radius of the pool. Considering the 55 degree angle, the fountain in your drawing is the opposite side (that’s the unknown) and the radius is the adjacent side. A tangent should give you the answer.
March 26th, 2011 - 12:07
Since the circumference is 2πr, solve for r using
2πr=25
r=25/(2π)
Imagine the fountain as the leg of a right triangle and the radius as another leg. The angle of elevation is 55º. You want to use tangent, because you know the adjacent side (the radius) and you are trying to find the oppiste side, the fountain’s height, let’s call it H.
tan(55º)=H/r
H=tan(55º)*r=tan(55º)*25/(2π)
Solve that on your calculator and you have your height. Make sure you put the right units in your answer (meters).