Question

Ellis built a window frame shaped like the top half of an ellipse. The window is 40 inches tall at its highest point and 160 inches wide at the bottom. What is the height of the window 20 inches from the center of the base?

Answer 1

Hi,

38.73 in

Explanation:

Equation of the ellipse is:

`(x^2)/(a^2) +(y^2)/(b^2) =1\ with\ a=80\ and\ b=40\\\\if\ x=20\ then\ \\\\(20^2)/(80^2) +(y^2)/(40^2) =1\\\\(y^2)/(40^2) =1-(1)/(16) \\\\y^2=40^2*(15)/(16) \ and \ y \ is \ positive\\\\y=40*(√(15) )/(4) \\\\y=10*√(15)\approx{38.73}`