Math/Trigonometry Question

[Jamey Saunders]

Don't take my word for this, because it's been 11 years since I had college trig, but...

If you know the distance from the chord to the apex (which, if I remember correctly is the center of the circle), and you know the length of the chord, then you know the lengths of the two legs of right triangles. The distance from the chord to the apex (let's call that X) and half the length of the chord (let's call the chord length Y) make up the sides of the triangle.

Knowing that, you could find the hypotenuse by solving C^2=X^2+(Y/2)^2. The hypotenuse would be the radius of the circle.

Where you go from here, I can't remember. But I do think I remember that there's a way to figure the opposing angle of a triangle if you know one angle (90*) and the lengths of a couple of sides. Once you've figured that angle, double it, and you've got the angle that includes the arc. Take that angle, and figure what percentage of the circumference it is. That percentage of the circumference of the circle should be the length of the arc.

That said, there's probably an easier way to do it. I'm waiting to see what others come up with.

[EDIT] Damn, Evan beat me to it, and he's much better than I am. Oh, well... [img]/images/graemlins/smirk.gif[/img]

[TBag]

Edit - btw x is chord height / 2.


I thought this worked, but Evan's is different.

When solving for radius, why do you divide by 2B?

[LaggyLou]

Hmmmm......maybe I'm not explaining it right. Here is the problem, and what I understand Evan's solution to be:
[image]http://img175.echo.cx/my.php?image=arcproblem5pq.png[/image]

Hmmm. I Can't figure out why the image tag isn't working. Try it as a
link.