Question

A bridge underpass in the shape of an elliptical arch, that is, half of an ellipse, is 40 feet wide and 13 feet high. An eight foot wide rectangular truck is to drive (safely) underneath. How high can

Answer 1

Answer:

The truck can be 12.7 feet high.

Step-by-step explanation:

This is half of an ellipse , where the major arc is : a = 20 feet  ( half of 40 feet ) and the minor arc is : b = 13 feet.

The equation of the ellipse :

x²/a² + y²/b² = 1

x²/ 400 + y²/ 169 = 1

Now we know that x = +/- 4

4²/400 + y²/169 = 1

16/400 + y²/169 = 1

y²/169 = 1 - 0.04

y²/169 = 0.96

y² = 0.96 · 169 = 162.24

y = √162.24 = 12.737 ≈ 12.7 feet.