We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.
Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:
x = 35 * cos(110)
y = 35 * sin(110)
Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:
d^2 = x^2 + (y + 150)^2
Plugging in the values for x and y, we get:
d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2
d^2 = 1225 + (150 + 35 * sin(110))^2
Using a calculator, we can find that sin(110) = 0.939, so:
d^2 = 1225 + (150 + 31.65)^2
d^2 = 1225 + (181.65)^2
d^2 = 1225 + 32762.7225
Taking the square root of both sides:
d = sqrt(1225 + 32762.7225)
d = sqrt(33987.7225)
d = 183.83
Rounding to the nearest yard:
d = 184 yards
So, the ball is 184 yards from the center of the green.