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23 September, 11:19

The radius of a circle is 8 inches. Find the number of radians in the central angle of the circle which intercepts an arc of 3 inches

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  1. 23 September, 11:42
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    The number of radians in the central angle is 0.375

    Step-by-step explanation:

    * Lets study the radians rule of the circle

    - If the measure of the central angle is Ф radians

    - If the length of the arc subtended by Ф is L

    ∴ L = r Ф

    * Lets look to the our problem

    ∵ The radius = 8 inches

    ∵ The measure of the central angle is Ф

    ∵ The length of the intercepted arc of Ф = 3 inches

    * Use the rule L = r Ф ⇒ divide both sides by r

    ∴ Ф = L/r

    ∴ Ф = 3/8 = 0.375 radians

    * The number of radians in the central angle is 0.375
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