A bridge is built in the shape of a semielliptical arch The

A bridge is built in the shape of a semi-elliptical arch. The base of the arch is 30 feet across, and the highest part of the arch 10 feet above the horizontal roadway. Find the exact height of the arch 6 feet from the center of the base. Leave the radical unsimplified.

X = 15, Y= 10, center is (0,0)
(x)^2/(15)^2+(y)^2/(10)^2 = 1

x = 6 implies
(36)/15^2+y^2/10^2 = 1
y^2/100 = 84/100
y = sqrt(84) = 2sqrt(21) = 9.165 ft