I have this question that I am stumped on, I have changed the numbers to a practice another version so that it is not the exact question on my homework.

An arch of a bridge is semielliptical, with major axis horizontal. The base of the arch is a across, and the highest part of the arch is b above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base. Assume a = 40 feet, b = 8 feet. (Round the answer to one decimal place.)

What I did..

wrote out my equation as (x^2/1600)+(y^2/64) = 1 from a^2 = 40^2 b^2 = 8^2

so i enter 7 in for x making it 49/1600 +y^2/64 = 1 that becomes sqrt ((1-49/1600) * 64)

that gives me the answer 7.9 however the answer key says 7.5 so where am i going wrong?