A high fountain of water is located at the center of a circular pool as shown in the figure below. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 39.0 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

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To find the height of the fountain, you can use trigonometry. Let's break down the problem step by step:

Step 1: Find the radius of the circular pool
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 39.0 m. Therefore, we can rearrange the formula to solve for the radius: r = C / (2π).
Plugging in the given circumference: r = 39.0 m / (2π) = 6.21 m.

Step 2: Calculate the distance from the edge of the pool to the fountain
To do this, we need to find the length of the arc formed by the angle of elevation at the bottom of the fountain. The arc length can be calculated by using the formula: arc length = (θ/360°) × 2πr, where θ is the angle in degrees.
Plugging in the given angle of elevation: arc length = (55.0°/360°) × 2π(6.21 m).

Step 3: Determine the height of the fountain
Since the arc length is equal to the distance from the edge of the pool to the fountain along the curved path, we can consider this as the height of the fountain.
Height of the fountain = arc length = (55.0°/360°) × 2π(6.21 m).

Now we can calculate the height of the fountain by plugging in the values in the above formula and performing the calculation.