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Math Help - word problem

  1. #1
    Junior Member
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    Unhappy word problem

    A circular wire of radius 15cm is cut and bent so as to lie along the circumference of a loop of radius 120cm .Write the measure of the angle subtended by it at the center of the loop.

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  2. #2
    Super Member Matt Westwood's Avatar
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    Draw a picture first, so you see what it's asking.

    2 pi times 15cm is the arc length of a circle radius 120 cm subtended by angle A.

    The full circle ix 2 pi and the full circumference is 2 pi times 120.

    Thus it's \frac {2 \pi \times 15}{2 \pi \times 120} and that's in radians, so you need to multiply by \frac {180} {\pi} to get the number of degrees.
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  3. #3
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    This is how I read this problem, there are 2 circles.

    One has a radius of 15cm which gives a circumference of 30\pi

    The other has radius of 120cm which gives a circumference of 240\pi

    The angle will be the proportion of the circumference of circle 1 around the circumference of circle 2

    Spoiler:
    \frac{30\pi}{240\pi}\times 360
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  4. #4
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    Quote Originally Posted by Matt Westwood View Post
    15cm is the arc length of a circle radius 120 subtended by angle A.

    The full circle ix 2 pi and the full circumference is 2 pi times 120.
    I read this to be the radius of the first circle.
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  5. #5
    Super Member Matt Westwood's Avatar
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    Sorry pickslides, I misread it to start with, I've edited my answer, thx.
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