Answer:
The total length of the string is 7.85 feet and the center should be 2.236 feet far the string be nailed into the base
Step-by-step explanation:
Circumference of ellipse = [tex]\pi(a+b)[/tex]
Circumference of semi-ellipse = [tex]\frac{\pi(a+b)}{2}[/tex]
we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.
So, [tex]a = \frac{6}{2}=3 , b = 2[/tex]
Circumference of semi-ellipse =[tex]\frac{3.14(3+2)}{2}=7.85 feet[/tex]
Distance from center =[tex]\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=2.236 feet[/tex]
Hence the total length of the string is 7.85 feet and the center should be 2.236 feet far the string be nailed into the base
