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Math Help - Finding the radius with just the chord length and central angle :)

  1. #1
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    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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Belinda View Post
    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
    Attached Thumbnails Attached Thumbnails Finding the radius with just the chord length and central angle :)-gash.jpg  
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Belinda View Post
    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)
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  4. #4
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    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.
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