Sally bought a sprinkler that squirts in a circular direction. With the center of the sprinkler as the center, it sends out water far enough to reach a point located at (12,16). If Sally's backyard is 40 feet long by 50 feet wide, about what percent of the backyard will NOT be watered directly? (Hint: Find area of circle and divide by area of yard to determine the percent that IS covered by the water)

Answer:37% of the backyard will not be covered by the water from the sprinkler.Step-by-step explanation:The sprinkler is at the centre (0,0). It squirts in a circular motion. The other end of the radius is at (12,16). First we will calculate the radius of the circle.[tex]r = \sqrt{(12-0)^2 + (16-0)^2}\\r = \sqrt{144 + 256}\\r = \sqrt{400}\\r = 20[/tex]Area of the circle = πr^2= 3.1416*(20)^2= 3.1416*400= 1256.64Area of yard = 40 ft * 50 ft= 2000Percent covered by the water = 100*(area of circle/area of yard)= 100*(1256.64/2000)= 100*(0.628)= 62.8%= 63%Area not covered by the water = 100 - 63= 37%