The posts of a hockey goal are 6 ft apart. A player attempts to score by shooting the puck from a point that is 19 ft from on of the posts and 24 ft from another post. Within what angle, must the shot be made. Express you answer to the nearest degree

Question

zepdrix · Answer

Oh still stuck on this one? :D

anonymous · Answer

Yea :( I wrote it out last night but it didn't work out

zepdrix · Answer

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Law of Cosines states that:$$\huge c^2=a^2+b^2-2ab \cos C$$ Applying this to our problem, we get:$$\huge 6^2=19^2+24^2-2(19)(24)\cos C$$ And from here, we need to solve for C.

zepdrix · Answer

Subtracting some stuff... we get.
$$\huge 6^2-19^2-24^2=-2(19)(24)\cos C$$And thennnn dividing some stuff, we get.. $$\huge \frac{6^2-19^2-24^2}{-2(19)(24)}=\cos C$$

zepdrix · Answer

Anddddddd simplifying it down gives us, $$\huge \frac{-901}{-912}=\cos C$$Canceling out the negatives gives us,$$\huge \frac{901}{912}=\cos C$$

zepdrix · Answer

Then the last step is a little tricky! :)
We can rewrite this expression using the inverse function, or we can simply take the inverse cosine of both sides. Let's try doing that.
$$\huge \cos^{-1}\left(\frac{901}{912}\right)=\cos^{-1}(\cos C)$$

zepdrix · Answer

$$\huge \cos^{-1}(\cos C)=C$$

zepdrix · Answer

$$\huge C=\cos{-1}\left(\frac{901}{912}\right)$$Last step is to simply plug this into your calculator, make sure you're in degree mode! :D

anonymous · Answer

Ohh ok I see where I went wrong here. Well thank you for your help :D