An arch for a bridge over a highway is in the form of a semi ellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 27 feet from the center is to be 15 feet above ground? Round to two decimal places

The span of the bridge is 59.77ft

Step-by-step explanation:

The standard form of equation for an ellipse with vertical major axis is:

(x-h)^2/b^2+(y-k)^2/a^2=1,a>b, (h,k)=(x,y) coordinates of center.

For given problem:

Place center of ellipse, (0,0) at center of bridge at ground level.

Given length of vertical major axis=70=2a

a=35

a^2=1225

Equation of an ellipse with horizontal major axis with center at (0,0)

Equation of ellipse:

x^2/b^2+y^2=1

plug in coordinates of given point on ellipse(27, 15)

27^2/b^2+15^2/a^2=1

729/b^2+225/1225=1

729/b^2=1-225/1225= 0.816

b^2=729/0.816≈ 893

b≈29.88

length of minor axis=2b≈59.77 ft

span of bridge≈59.77 ft