1)A 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.
The answer given is-
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Draw a line from the golfer to the hole 195m
Draw another line off at 10 degrees length 170m
Draw a perpendicular connecting the two giving a triangle. Draw another triangle connecting the ball to the tee using the rest of the 195m direct line.
c |__\ Ball (line to ball is the perpendicular b)
195m | /
a | / h = 170m
Use trigonometry relation cos(theta) = a/h
'a' is the length directly from the golfer to the perpendicular going off to the ball, theta is 10 degrees and h is 170m
So a = 170*cos(10) m = 167m
b is the length of the perpendicular sqrt(170^2-a^2) = 29.5m using pythagoras' theorem a^2+b^2=h^2
c is the length 195m - a = 27.56m
d is the distance between the ball and the hole, ie what we want.
Again using pythagoras d = sqrt(b^2 + c^2) = 40.4m