EXPLANATION
We can apply the Pythagorean Theorem as shown as follows:
[tex]c^2=a^2+b^2[/tex]
If the radius is 20 ft, then c=20 ft
If CD = 32 ft, then b= CD/2 = 32/2 = 16 ft
Replacing terms:
[tex]20^2=a^2+16^2[/tex]
Isolating a:
[tex]20^2-16^2=a^2[/tex]
Computing the powers:
[tex]400-256=a^2[/tex]
Applying the square root to both sides:
[tex]\sqrt[]{400-256}=a[/tex]
Simplifying:
[tex]\sqrt[]{144}=12=a[/tex]
The measure of AB is 12*2= 24 ft long
