high fountain of water is located at the center of a circular pool as in the figure. A student walks around the pool and estimates its circumference to be 212 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 53.7◦.
How high is the fountain? Answer in units of m
Think if you were standing on top of the fountain. The distance from the fountain to the edge would be the radius of a circle or the base of a triangle. The triangle would consist of the base, which is the radius of the pool, the height of the fountain would be the opposite side of the triangle.
The base of the triangle, or the adjacent side, would equal the radius of the fountain.
Since we have the circumference, C = 212m, we need to find the radius which equals 1/2 of the diameter.
Thus the diameter is = C/pi = 212/3.14 = 67.48 meters.
The radius R = 1/2 D = .5 X 67.48 = 33.9m
Since we have the base of the triangle and the angle, we can find the height
The height of the triangle =
tan 53.7 multiplied by the adjacent side=1.361335036296 multiplied by33.9 = 46.14m
