Solve the problem.
-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. What should the span of the bridge be, rounded to the nearest hundredth of a foot, if the height 32 feet from the
Center is to be 16 feet above ground?
A) 71.96 ft
B) 140 ft
C) 79 ft
D) 35.98 ft

Question

Quizplus · Accepted Answer

The equation of an ellipse centered at the origin with a vertical major axis is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. Here, $a = 35$ (half the height of the arch) and we are given that when $x = 32$, $y = 19$ (since the height above ground is 16 feet, and the total height is 35 feet, the distance from the center to the point is $35 - 16 = 19$ feet). Plugging these values into the ellipse equation, we solve for $b$, and then double it to find the span of the bridge. The correct calculation leads to a span of approximately 71.96 feet.

Solve the Problem. -An Arch for a Bridge Over a Highway Is in Highway