Determine angle from radius of curvature

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This is another grade school problem that's giving me trouble (posting on someone else's behalf).

I can see that a 36 inch semi-circumference yields a radius of 36/Pi or about 11.46 inches.

However, I can't see how to use this information to calculate the angle. Given the width of the arch, I may be able to do this, but don't see an easy solution otherwise.

Given that this is a grade school problem, I'm obviously missing something basic.

Using the "eyeball theorem" (ha ha), it seems like that angle is 172 degrees (it's clearly not 85 or 100 obviously).

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2 Answers

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The formula is $r a = s$ where $r$ is the radius, $s$ is the arc length, and $a$ is the central angle in radians.

So the angle is $36/12 = 3$ radians, which is about $172$ degrees (multiply by $\pi/180$).

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The length of an arc of angle $\theta$ radians and radius $r$ is $r\theta$. And $\pi \neq 22/7$

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