On a dogleg golf hole, one golfer hits the ball 260 yards and then another 160 yards to reach the green. The angle between the two hits is equal to 100 degrees. How far would the golfer have to originally hit the ball for it to go directly to the same position on the green?

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07-03-2022
Mathematics

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On a dogleg golf hole, one golfer hits the ball 260 yards and then another 160 yards to reach the green. The angle between the two hits is equal to 100 degrees. How far would the golfer have to originally hit the ball for it to go directly to the same position on the green?

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Topeadeniran2idn Topeadeniran2idn · Answer 1 · 2022-03-16T14:50:36-04:00

The distance that the golfer have to originally hit the ball for it to go directly to the same position is 302.91 yards.

How to calculate the distance?

From the information given, a golfer hits the ball 260 yards and then another 160 yards to reach the green and the angle between the two hits is equal to 100 degrees.

According to cosine law, the distance to use will be:

d² = 260² + 160² - 2 × 260 × 160 cos 100°

d² = 67600 + 25600 - 83200(0.1736)

d² = 93200 - 14443.52

d² = 91756.48

d = 302.91 yards.

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