Not homework, but I need to figure this out...

[Guest]

Ok, this is not homework, and to my slight shame, I actually have had a minor in math for quite a while and I'm just not figuring this out. I guess it's a matter of use it or lose it. This is a trigonometric problem that relates to a problem for a multiplayer game that relates to a website I'm working on. If this forum is for homework questions only, my apologies and feel free to move it. But if anyone here enjoys solving math problems, and I'm sure someone does here ya go.

See this chart:

http://www.secretsofbattlefield.com/claymorechart.jpg

Take a look at this image and let's make a few assumptions: First of all, this sort of conic shape is actually a slice of a big invisible circle. That much is in fact true, as I have confirmed from testing -- so, the little hasmarks implying it terminates before it reaches the center of the circle are deceptive.

Next, let's assume the "12 feet" value is the length of the outer circumfrence line for the red area. That much should be true. Next, let's assume the "9 feet" value is the length of the line you would get if you drew a straight line from the starting point on the 12-foot line to the ending point on the 12-foot line. See the screenshot and hopefully this all makes sense.

Can anybody remind me how to calculate -- or if you're in a good mood, simply calculate the angular radius of the red area as it extends from the central point on the circle, the radius, and the effective area of the red area? Thanks for helping me out, guys. I feel kind of stupid for not being able to do this, since I've had training all the way through linear algebra and DEQs.

 

[galactus]

I am not totally clear on what you're asking, but if you want the angle subtended by the arc length(12) and the given chord(9):

\(\displaystyle \L\\Long chord=2Rsin(\frac{{\theta}}{2})\\9=2Rsin(\frac{{\theta}}{2})\) (1)

Length of arc:

\(\displaystyle \L\\S=R{\theta}\\12=R{\theta}\) (2)

You have two equations with two unknowns.

Solve (2) for \(\displaystyle {\theta}\):

\(\displaystyle {\theta}=\frac{12}{R}\)

Sub into (1):

\(\displaystyle 9=2Rsin(\frac{6}{R})\)

Solving for R, we get Radius=4.7 and \(\displaystyle {\theta}=2.55\ radians\)

or 146.18 degrees.


Is this want you were looking for?.

 

[Guest]

I am sure your math is right, but the information I have given you must be wrong, as the final angle will most definitely be roughly 30-45 degrees. But thank you for showing me how you did the math as I should be good to go, now.

 

[Denis]

180 - 146.18 = 33.82