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A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of the green. While
standing on the marker and facing the green, the golfer turns 100° towards his ball. He then paces off 30 yards to his ball. How far is the
ball from the center of the green?
150 yd

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Starrysoul100

[tex]\bold{\huge{\underline{ Solution}}}[/tex]

Given :-

  • A marker in the center of the fairway is 150 yards away from the centre of the green
  • While standing on the marker and facing the green, the golfer turns 100° towards his ball
  • Then he peces off 30 yards to his ball

To Find :-

  • We have to find the distance between the golf ball and the center of the green .

Let's Begin :-

Let assume that the distance between the golf ball and central of green is x

Here,

  • Distance between marker and centre of green is 150 yards
  • That is, Height = 150 yards
  • For facing the green , The golfer turns 100° towards his ball
  • That is, Angle = 100°
  • The golfer peces off 30 yards to his ball
  • That is, Base = 30 yards

According to the law of cosine :-

[tex]\bold{\red{ a^{2} = b^{2} + c^{2} - 2ABcos}}{\bold{\red{\theta}}}[/tex]

  • Here, a = perpendicular height
  • b = base
  • c = hypotenuse
  • cos theta = Angle of cosine

So, For Hypotenuse law of cosine will be :-

[tex]\sf{ c^{2} = a^{2} + b^{2} - 2ABcos}{\sf{\theta}}[/tex]

Subsitute the required values,

[tex]\sf{ x^{2} = (150)^{2} + (30)^{2} - 2(150)(30)cos}{\sf{100°}}[/tex]

[tex]\sf{ x^{2} = 22500 + 900 - 900cos}{\sf{\times{\dfrac{5π}{9}}}}[/tex]

[tex]\sf{ x^{2} = 22500 + 900 - 900( - 0.174)}[/tex]

[tex]\sf{ x^{2} = 22500 + 900 + 156.6}[/tex]

[tex]\sf{ x^{2} = 23556.6}[/tex]

[tex]\bold{ x = 153.48\: yards }[/tex]

Hence, The distance between the ball and the center of green is 153.48 or 153.5 yards

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