On a 180-yard hole, a golfer hits the ball 175 yards, 3 degrees off-line. How far is the ball from the cup?

## On a 180-yard hole, a golfer hits the ball 175 yards, 3 degrees off-line. How far is the ball from the cup?

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# 1 Answer

You can set this up using the law of cosines.

Recall that the law of cosines is **c ^{2} = a^{2} + b^{2} -2ab cos θ** where

**θ**is the angle included between sides of lengths

**a**and

**b**while

**c**is the remaining side's length.

In this case we have **a** = 175, **b** = 180, and **
θ** = 3°

So the final distance is

**c** = √(175^{2} + 180^{2} - 2·175·180 cos 3°) = 10.6 yards