Question

In playing from the tee, a golfer hooks his drive (hits the ball to the left of the correct direction) at an angle of 24 from the intended direction. He estimates that he has driven the ball 215 yards and that it lies 100 yards from the hole. Assuming his estimates are correct, what is the distance from the tee to the hole, to the nearest yard?

Answer 1

245 yards

Explanation:

Answer 2

245 yards

Explanation:

You could say the tee is at (0, 0) and the hole lies on the x-axis.

The path of the ball is the straight-line so, y = tan(24°)x

215cos(24°) = 196.4

215sin(24°) = 87.4

The ball lands at coordinates (196.4, 87.4).

They say the ball lands 100 yards from the hole, the hole is on a circle of radius 100 that is centered at (196.4, 87.4).

Equation of the circle:

(x-196.4)² + (y-87.4)² = 100²

Since the hole is on the x-axis, it lies at the intersection of the circle and the line y = 0 so:

(x - 196.4)² + (0 - 87.4)² = 100²

x = 244.92

The distance between tee and hole is 245 yards.