Question

A bridge witha semi-elliptical arch spans a river as shown here. What is the clearance 7ft from the riverbank ?

Answer 1

`\begin{gathered} By\text{ solving using the equation of an Ellipse} \\ (x^2)/(a^2)+\text{ }(y^2)/(b^2)\text{ = 1} \\ a\text{ = }(46)/(2)\text{ = 23 x = 23 -7 =16} \\ b\text{ = 14} \\ (x^2)/(a^2)+\text{ }(y^2)/(b^2)\text{ = 1} \\ (16^2)/(23^2)+(y^2)/(14^2)\text{ = 1} \\ (256)/(529)+\text{ }(y^2)/(196)\text{ = 1} \\ (y^2)/(196)\text{ = 1 -}(256)/(529) \\ (y^2)/(196)\text{ = 0.516} \\ y^2\text{ = 196 x 0.516} \\ y^2\text{ = 101.56} \\ \text{y = }\sqrt[]{101.56}\text{ = 10.06feet} \end{gathered}`