[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
