high fountain of water is located at the center of a circular pool. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 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 ?
radius=15/2PI
tan55=h/r
h= r tan 55
h=r.tan a=1/2pi.tan a=15m/2pi.tan55deg.=3.41m
I need proper solutions
To determine the height of the fountain, we can use trigonometry. Let's break down the problem into two scenarios:
1. Measurements around the pool:
The circumference of a circle (C) is given by the formula: C = 2πr, where r is the radius of the circle.
In this case, the student measures the circumference of the pool to be 15.0 m. So, we can write the equation as:
15.0 m = 2πr
We need to find the radius of the pool (r) to calculate the height of the fountain. Rearranging the equation, we have:
r = 15.0 m / (2π) ≈ 2.39 m
2. Angle of elevation at the bottom of the fountain:
Now, using the angle of elevation, we can create a right-angled triangle with the height of the fountain (h) as the opposite side and the radius of the pool (r) as the adjacent side. The angle of elevation is 55.0°.
We know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right-angled triangle. So, we can write the trigonometric equation as:
tan(55.0°) = h / r
Substituting the values we have:
tan(55.0°) = h / 2.39 m
Rearranging the equation, we can solve for h:
h = tan(55.0°) * 2.39 m ≈ 3.28 m
Therefore, the height of the fountain is approximately 3.28 meters.