# 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...

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-

40.4m

if possible please provide your answer with a diagram and upload on some website like - www.imagetoo.com.So i can refer to it

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### 1 Answer

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.

Tee

|\ d

c |__\ Ball (line to ball is the perpendicular b)

195m | /

a | / h = 170m

| /

|/

Golfer

Note a+c=195m

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