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Circles

SAT Math· difficulty 4/5

On a circle, an arc has length 5pi5\\pi and the radius is 6. What is the central angle in degrees?

  • A

    120°120°

  • B

    60°60°

  • C

    30°30°

  • D

    150°150°

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Explanation

Arc length =fractheta360°(2pir)= \\frac{\\theta}{360°}(2\\pi r). So 5pi=fractheta360°(12pi)5\\pi = \\frac{\\theta}{360°}(12\\pi), giving theta=frac5picdot360°12pi=150°\\theta = \\frac{5\\pi \\cdot 360°}{12\\pi} = 150°.

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