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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?

Respuesta :

carlosego
The first thing we must take into account is that the circumference of the pool is given by:
 2 * pi * R = 190
 From here, we clear the radio:
 R = (190) / (2 * pi)
 R = 30.23943919 m
 Then, you can see the problem as a rectangle triangle, where the height of the source will be given by the following trigonometric relationship:
 tan (55) = H / R
 From here, we clear the height H:
 H = R * tan (55)
 H = (30.23943919) * tan (55)
 H = 43,1863948 m
 Amswer:
 the fountain is 43.19 m high

The height of the fountain is 43.20m

Data;

  • circumference = 190m
  • angle = 55 degrees.

Circumference of a Circle

The circumference of a circle is given as

[tex]c = 2\pi r[/tex]

Let's calculate the radius of the circle

[tex]c=2\pi r\\r=c/2\pi \\r=190/(2*3.14)\\r=30.25m[/tex]

Assuming the radius of the pool makes a right angle triangle with the top of the fountain;

[tex]tan\theta=\frac{opposite}{adjacent}\\tan55=\frac{x}{30.25}\\ x= 30.25tan55\\x=43.20m[/tex]

From the calculations above, the height of the fountain is 43.20m

Learn more on right-angle triangles here;

https://brainly.com/question/22790996