Question

a golfer hits an errant tee shot that lands in the rough. a marker in the center of the fairway is 120 yards from the center of the green. while standing on the marker and facing the green, the golfer turns 110° towards his ball. he then paces off 45 yards to his ball. how far is the ball from the center of the green?
the ball is about \\(\square\\) yards from the center of the green.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the triangle sides and angle

We have a triangle with two sides: \( a = 120 \) yards (marker to green), \( b = 45 \) yards (marker to ball), and the included angle \( C = 110^\circ \). We use the Law of Cosines: \( c^2 = a^2 + b^2 - 2ab\cos(C) \).

Step2: Substitute values into the formula

Substitute \( a = 120 \), \( b = 45 \), and \( \cos(110^\circ) \approx -0.3420 \) into the formula:
\( c^2 = 120^2 + 45^2 - 2(120)(45)\cos(110^\circ) \)
\( c^2 = 14400 + 2025 - 2(120)(45)(-0.3420) \)
\( c^2 = 16425 + 3717.6 \)
\( c^2 = 20142.6 \)

Step3: Solve for \( c \)

Take the square root: \( c = \sqrt{20142.6} \approx 141.9 \) (rounded to one decimal place).

Answer:

141.9