Question

In a model, it is shown that an arc of a bridge is semielliptical with major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from horizontal, the best approximation of the height of the arch, 2m from the center of the base is:

• A. 11 m
• B. 8 m
• C. 7 m
• D. 2 m

Hint:

For problems involving semielliptical arches, use the standard equation of an ellipse to calculate the height at any given point.

Answer 1

The Correct Option is B

Step 1: Use geometry of semielliptical arch. For a semielliptical bridge, use the equation of the ellipse to approximate the height of the arch at the given point.
Step 2: Conclusion. Thus, the height of the arch at 2m from the center is approximately 8 m.