A golfer consistly drives a golf ball 190m. if she hits her ball down a fairway that is 83 m wide what is the maximum angle between a drive to the left and a drive to the right that would still be on the fairway.

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- Sep 14th 2010, 09:50 PMwinsomeAlgebra
A golfer consistly drives a golf ball 190m. if she hits her ball down a fairway that is 83 m wide what is the maximum angle between a drive to the left and a drive to the right that would still be on the fairway.

- Sep 14th 2010, 09:56 PMUnknown008
I suggest you make a sketch of the situation.

You'll end up with a triangle with height 190 m and a perpendicular base to this height of 83m

You can half the length of the base, to get 41.5 m.

Then, you know that the angle (theta) for the between the central line and the left drive is given by:

$\displaystyle tan(\theta) = \frac{41.5}{190}$

$\displaystyle \theta = tan^{-1}(\frac{41.5}{190})$

Then, the maximum angle between the drive to the left and the drive to the right is twice that angle.

$\displaystyle Maximum\ angle = 2\theta = 2tan^{-1}(\frac{41.5}{190})$

I got $\displaystyle 24.6^o$ - Sep 14th 2010, 10:59 PMwinsome
You write half the length of the base, is 41.5 m but in calculation used 43.1

how it is possible ? i think it should be 41.5. - Sep 14th 2010, 11:05 PMUnknown008
Oops, right, a typo from me. Sorry for that. I'll edit my post.

- Sep 14th 2010, 11:12 PMwinsome
thanx to listen me.