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paleeoguy
paleeoguy asked in Science & MathematicsMathematics · 1 decade ago

Finding Central Angle and Radius?

Hi. I've been working on this problem for the last 45 minutes and I'm at a wall and would really appreciate a nudge in the right direction. It seems straightforward enough:

In the figure, the arc length is 52 and the chord length is 40. Find the central angle and the radius.

Here is a link with a pic of the figure I drew.

http://picasaweb.google.com/lh/photo/BB6dqgVM928tG...

Any help would be awesome.

Thanks.

Update:

Here's what the book gives as an answer:

Theta (central angle) = 2.1

r = 24

Any clue how those come up?

Update 2:

Oh, and this is all in Radians.

2 Answers

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  • Merlin
    Lv 7
    1 decade ago
    Favorite Answer

    If the sides of the triangle are called a, b and c and side a is the chord, then a = 40. Sine Law says

    SinA/a = SinB/b = SinC/c

    SinA/40 = SinB/(radius) = SinC/(radius)

    Also, angles B and C are equal

    360 - (B + C) = A

    But I don't see how more can be solved without more information.

  • barefoot_blonde
    1 decade ago

    the central angle would be 52 if the arc is an inscribed arc. the radius is one of the legs of the triangle. and since the triangle's legs are both the radius' then they would be equal. hope this helps

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