A student walks around a pool and estimates the pool has a circumference of 240 m.
Using a protractor the students gages the angle of elevation to the top of the fountain, in the center of the pool, to be 74 degrees.
This question in incomplete. Do they want to know the height of the fountain?
That would be H = R*tan74, where
R = 240/(2 pi) = 38.2 meters.
Now compute H.
It seems rather high to me.
Oh, yes. I am sorry.
I am attempting to calculate the height of the fountain.
It does indeed seem rather high. But the numbers for my assignment are randomly generated. So that may explain this phenomenon.
Thank you for your help.
So what is your question? I'm assuming
you want to know the height of the fountain.
C = 6.28r = 250m,
r = 250 / 6.28 = 39.8m.
tan74 = h/r = h / 39.8
h = 39.8tan74 = 138.8m.
drwls, you finished a little ahead of me: but that's good because i used the wrong value for the circumference.
To find the height of the fountain, we can use trigonometry. Let's break down the problem step by step:
Step 1: Visualize the scenario
Imagine a circular pool with a fountain at its center. The student is standing somewhere around the pool and looking at the fountain. The angle of elevation is the angle between the student's line of sight and the horizontal plane.
Step 2: Understand the information given
The student estimates the circumference of the pool to be 240 meters. This means that if the student walks around the pool, they would have to cover a distance of 240 meters. Additionally, the student measures the angle of elevation to the top of the fountain and finds it to be 74 degrees.
Step 3: Identify the trigonometric ratio
Since we have the angle of elevation, let's focus on the opposite and adjacent sides of the triangle formed. The opposite side is the height of the fountain (which we want to find), and the adjacent side is the radius of the pool.
Step 4: Set up the trigonometric equation
We'll use the tangent function, which relates the opposite side to the adjacent side. In this case, the tangent of the angle of elevation (74 degrees) is equal to the height of the fountain (opposite side) divided by the radius of the pool (adjacent side).
tan(74 degrees) = height of fountain / radius of pool
Step 5: Solve the equation
To find the height of the fountain, we need to isolate that variable. We rearrange the equation:
height of fountain = tan(74 degrees) * radius of pool
Step 6: Calculate the height of the fountain
We know the circumference of a circle is related to its radius by the equation:
circumference = 2π * radius of pool
240 meters = 2π * radius of pool
Solving for the radius of the pool:
radius of pool = 240 meters / (2π)
Now, substituting this value into the equation we derived earlier:
height of fountain = tan(74 degrees) * (240 meters / (2π))
Using a calculator, we can evaluate:
height of fountain ≈ tan(74 degrees) * (240 meters / (2π))
Please note that the height of the fountain will be in meters, and the result will depend on the specific values of tan(74 degrees) and π used for calculations.