A high fountain of water is in the center of a circular pool of water. You walk the circumference of the pool and measure it to be 190 meters. You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. It is 55°. How high is the fountain?Select one:a.86 mb.43 mc.53 md.48 me.25 m
Question
A high fountain of water is in the center of a circular pool of water. You walk the circumference of the pool and measure it to be 190 meters. You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. It is 55°. How high is the fountain?Select one:a.86 mb.43 mc.53 md.48 me.25 m
Solution
To solve this problem, we need to use some trigonometry.
First, we need to find the radius of the pool. We know that the circumference of a circle is given by the formula 2πr, where r is the radius. So, we can find the radius by dividing the circumference by 2π.
190 m / 2π = 30.2 m
Next, we use the tangent of the angle of elevation to find the height of the fountain. The tangent of an angle in a right triangle is equal to the opposite side (the height of the fountain, in this case) divided by the adjacent side (the radius of the pool).
So, we have:
tan(55°) = height / 30.2 m
Solving for height gives us:
height = tan(55°) * 30.2 m = 40.8 m
So, the height of the fountain is approximately 40.8 meters. However, this option is not available in the choices given. The closest option to this value is 43 m. Therefore, the answer is:
b. 43 m
Similar Questions
A water fountain is designed to shoot a stream of water in the shape of a parabolic arc. The equation of the parabola is given by ℎ(𝑡)=−0.5𝑡2+4𝑡+1h(t)=−0.5t 2 +4t+1, where ℎ(𝑡)h(t) represents the height of the water stream in meters and t represents the time in seconds since the water was shot. Answer the following questions.Determine the maximum height reached (in meters).
Isabella is making a huge flag of her country, the Republic of Seychelles, on a canvas by meters long. To do that, she has to draw a diagonal that begins at the bottom-left corner and ends at the right side of the flag, at a height of meters. Since the ends of the diagonal are too far to put a ruler between them, Isabella wanted to find the angle of the diagonal and draw it using a protractor. What is the angle of elevation, in degrees, of the diagonal? Round your final answer to the nearest tenth.
The approximate volume of a cylindrical water tower is 7,540 ft3. The diameter of the water tower is 20 ft. What is the approximate height of the water tower?
A water main is to be constructed with a 10% grade in the north direction and a 25% grade in the east direction. Determine the angle theta required in the water main for the turn from north to east. provide the answer in radians, round to the nearest hundredth as needed.
Larissa dives into a pool that is 8 feet deep. She touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water. What is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.