# Thread: Finding a formula for degrees measurements

1. ## Finding a formula for degrees measurements

I am looking for a formula/method to solve angular measuremnt problems in circles, any help of advising of a formula/method would be appreciated.

Example,

I have a circle, in the circle is a arc O to A and O to B, the arc is a minor arc. I know the length of the arc, and I know the length of the radius, what I want to know is the formula/method to work out the angle subtended by this arc?

I know the angle in the attachment is 90 degrees, but the angle in my problem is an obtuse angle in the circle. The attachment is for guidance only.

I have not given more information because I wish to solve the problem myself before anyone else solves it for me.

Thanks

David

2. ## Re: Finding a formula for degrees measurements

Originally Posted by David Green
I am looking for a formula/method to solve angular measuremnt problems in circles, any help of advising of a formula/method would be appreciated.

Example,

I have a circle, in the circle is a arc O to A and O to B, the arc is a minor arc. I know the length of the arc, and I know the length of the radius, what I want to know is the formula/method to work out the angle subtended by this arc?

I know the angle in the attachment is 90 degrees, but the angle in my problem is an obtuse angle in the circle. The attachment is for guidance only.

I have not given more information because I wish to solve the problem myself before anyone else solves it for me.

Thanks

David
In radians the formula is $l = r \theta \Leftrightarrow \theta = \dfrac{l}{r}$ where $l$ is the arc length, $r$ is the radius and $\theta$ the angle subtended.

If you can find an expression to change radians to degrees you can manipulate that formula

3. ## Re: Finding a formula for degrees measurements

Originally Posted by e^(i*pi)
In radians the formula is $l = r \theta \Leftrightarrow \theta = \dfrac{l}{r}$ where $l$ is the arc length, $r$ is the radius and $\theta$ the angle subtended.

If you can find an expression to change radians to degrees you can manipulate that formula
Thanks for the info;

so I understand that my obtuse angle is now worked out at 114.6 degrees, but the answers given, only one will be correct are are either fractions, fractions with pie or decimals?

so if I say;

114.6 / 360 = 0.32 x pie = 1, if this answer was correct it could be a typical decimal answer, but if a fraction like 1/2 pie, how would I convert to that method?

Thanks

David

4. ## Re: Finding a formula for degrees measurements

Originally Posted by David Green
Thanks for the info;

so I understand that my obtuse angle is now worked out at 114.6 degrees, but the answers given, only one will be correct are are either fractions, fractions with pie or decimals?

so if I say;

114.6 / 360 = 0.32 x pie = 1, if this answer was correct it could be a typical decimal answer, but if a fraction like 1/2 pie, how would I convert to that method?

Thanks

David
We can use the formula above to show that a full circle subtends an angle of $2\pi$ radians. Naturally, this is equal to 360 degrees: $2\pi^c = 360^o$ and after cancelling by 2 we get $\pi = 180^o$ as well as $1 rad = \dfrac{180}{\pi}^o$ and $1^o = \dfrac{\pi}{180} rad$

Thus your angle of 114.6 degrees is $\dfrac{114.6\pi}{180}$

I would take the expression saying $1 rad = \dfrac{180}{\pi}^o$, multiply by theta to give an expression for theta radians.
This can then be subbed into the equation in post 2 and then manipulated to give an expression for theta in terms of pi, 180, l and r

5. ## Re: Finding a formula for degrees measurements

Originally Posted by e^(i*pi)
We can use the formula above to show that a full circle subtends an angle of $2\pi$ radians. Naturally, this is equal to 360 degrees: $2\pi^c = 360^o$ and after cancelling by 2 we get $\pi = 180^o$ as well as $1 rad = \dfrac{180}{\pi}^o$ and $1^o = \dfrac{\pi}{180} rad$

Thus your angle of 114.6 degrees is $\dfrac{114.6\pi}{180}$

I would take the expression saying $1 rad = \dfrac{180}{\pi}^o$, multiply by theta to give an expression for theta radians.
This can then be subbed into the equation in post 2 and then manipulated to give an expression for theta in terms of pi, 180, l and r
Thanks for your help, I have worked out with your help previously and now confirmed with this thread that 114.6 x pie / 180 = gives the same answer as I have worked out, i.e. 2, which corresponds to the answer given.

Thank you

David