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.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

493 would be the correct answer

step-by-step explanation: