An arched footbridge over a 100-foot river is shaped like half an ellipse. The maximum height of the bridge over the river is 20 feet. Find the height of the bridge over a point in the river exactly 25 feet from the center of the river.

a.

15.45 ft

c.

17.32 ft

b.

16.25 ft

d.

19.24 ft

Please select the best answer from the choices provided

A

B

C

D

  c.  17.32 ft

Step-by-step explanation:

The attached graph provides a quick and easy solution.

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The equation of an ellipse with semi-major axis 50 and semi-minor axis 20 can be written as ...

  (x/50)^2 +(y/20)^2 = 1

We want to find the positive value of y when x=25.

  (25/50)^2 +(y/20)^2 = 1

  (y/20)^2 = 1 - 1/4 = 3/4 . . . . . subtract the constant on the left

  y = 20√(3/4) = 10√3 . . . . . . .square root and multiply by 20

The height of the bridge 25 feet from center is 10√3 ≈ 17.32 feet.