I need to know the circumference of a circle... hold on, its not THAT easy! lol?

Question

This one's for all you trigonometry experts. I need to find the diameter of a circle based on just two things: arc length and chord. The arc length is 24" and the chord is 20". Now, I can get the answer by trial and error, but what I want is the actual process. I would like the full equation so I can do it on my own later. In case you were wondering, I'm building a curved plexiglass enclosure. Thanks for your help! :-D

Answer 1

length of the arc s, length of the chord c

Solve

   c/s = sin(x)/x,

for x, which must be done numerically (see below). Then

   theta = 2x,

   radius= s/theta,

etc.

Answer 2

BUY an HP scientific calculator.

Answer 3

the two conditions that must be met are  r Θ = length of the arc and chord length joining the ends of the arc =√ ( (r cos Θ - r)² + r sin Θ)² )...in your given 24 = r Θ and 400 = 2 r² - 2 cos Θ..this is two equations in two unknowns and can be solved...most likely by a numerical process or by graphing of two r functions of Θ..I got r = 14.12 and Θ = 1.70..(about!)