Golfer hits his ball B a distance of 170m towards a Hole H which measures 195m from the Tee T to the green. If his shot is directed 10 degrees away from the true line to the hole, find the distance between his ball and the hole?
1
Expert's answer
2021-04-15T07:52:00-0400
Let AH is the length from the Golfer to the perpendicular going off to the ball, CA=170 m, BA=195 m, ∠A=10°.
CB is the distance between the ball and the hole.
1) Using right triangle trigonometry: cosx=hypotenuseadjacent and adjacent=hypotenuse∗cosx.
Then AH=CA∗cos∠A=170∗cos10°=167,4 m.
2) Using Pythagorean's theorem a2+b2=с2.
Then CH2+AH2=CA2
CH=CA2−AH2
CH=1702−167,42=29,5 m
3) BH=BA−AH
BH=195−167,4=27,6 m
4) Using Pythagorean's theorem a2+b2=с2.
Then CH2+BH2=CB2
CB=CH2+BH2
CB=29,52+27,62=40,4 m
Hence the distance between the ball and the hole is 40,4 m.
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