Thread: Finding the radius with just the chord length and central angle :)

Hello everyone,

I'm an product design that has come across a slight problem due to poor maths ability. I would like to find out the radius of a circle segment whilst only knowing the chord length (150) and the central angle (18°).

Please, if someone could help me solve this I would be extremely grateful. It's very frustrating since i've not done any trigonometry in years and it is vital for me to progress in my project.

Thank you for your time

Belinda

Originally Posted by Belinda

Hello everyone,

I'm an product design that has come across a slight problem due to poor maths ability. I would like to find out the radius of a circle segment whilst only knowing the chord length (150) and the central angle (18°).

Please, if someone could help me solve this I would be extremely grateful. It's very frustrating since i've not done any trigonometry in years and it is vital for me to progress in my project.

Thank you for your time

Belinda

Draw a diagram (see attachment).

From this we see that sin(9)=75/r, or r=75/sin(9). Now the sin of 9 degrees is ~= 0.1564,
so r ~= 479.4

RonL

Originally Posted by Belinda

Hello everyone,

I'm an product design that has come across a slight problem due to poor maths ability. I would like to find out the radius of a circle segment whilst only knowing the chord length (150) and the central angle (18°).

Please, if someone could help me solve this I would be extremely grateful. It's very frustrating since i've not done any trigonometry in years and it is vital for me to progress in my project.

Thank you for your time

Belinda

Just in case you come across another problem like this.

radius=(half the chord length)/(sin of half of the angle)

Thank you both for replying
I realised after posting that the simplest way to find out was to draw a diagram like captainblack suggested. Thank you for the equation quick.

I got 478 on my diagram, I thought I'd be way off.