Problem A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.

Answer Key

Solution

$\dfrac{x^2}{3^2} + \dfrac{y^2}{2^2} = 1$

At x = 1.5 $\dfrac{1.5^2}{9} + \dfrac{y^2}{4} = 1$

$y = 1.732 ~ \text{m}$ ← answer

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