Final answer:
The sprinkler can project water approximately 9.6 feet out, which rounds to 10 feet when looking for the nearest integer.
Step-by-step explanation:
To determine the distance that the sprinkler can project water out, we can use the formula for the area of a sector of a circle: A = (\theta/360) \times \pi r^2, where A is the area watered by the sprinkler, θ is the angle of rotation in degrees, and r is the radius of the circle, which corresponds to the distance the water travels.
The area A is given as 200 square feet and the angle θ is 135 degrees. Plugging these values into the formula and solving for r gives us:
A = (135/360) × π r^2
200 = (135/360) × π r^2
200 ÷ ((135/360) × π) = r^2
r^2 = 200 ÷ (0.375 × π)
r = √(200 ÷ (0.375 × π))
r ≈ 9.6 feet