Answer:
50.96 degrees
Step-by-step explanation:
step 1
Find the area of complete circle with radius 15 yards
The area of the circle is given by the formula
[tex]A=\pi r^{2}[/tex]
substitute the given value of r
[tex]A=\pi (15)^{2}[/tex]
[tex]A=225\pi\ yd^2[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]A=225(3.14)=706.5\ yd^2[/tex]
step 2
Through what angle should the sprinkler rotate?
we know that
The area of the complete circle subtends a central angle of 360 degrees
so
using proportion
Find out the central angle of a sector of 100 square yards
[tex]\frac{706.5}{360^o}=\frac{100}{x} \\\\x=360(100)/706.5\\\\x= 50.96^o[/tex]
