a tent in form of semi ellipse with width of the base 16 meters, its height 20/3 meters.

Question

what is the width of the tent at the height of 10/3 meters from the base

with steps

Answer 1

The base is twice the length of the semi-major axis, while b=20/3 metres is the length of the semi-minor axis.

Semi-major axis, a=8m.

The equation of the ellipse is x²/a²+y²/b²=1, x²/64+9y²/400=1. When y=10/3, x²/64+(9/400)(100/9)=1, x²/64=1-¼.

x²=48, x=±4√3=±6.93m approx. So width of the tent at height 10/3 m is 6.93×2=13.86m approx.