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geometry

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A park maintenance person stands 16 m from a circular monument. Assume that her lines of sight form tangents to the monument and make an angle of 47°. What is the measure of the arc of the monument that her lines of sight intersect? Please don't just answer it tel me how to do it. Thanks :)

  • geometry -

    P = 47 Deg.
    Arc AB is the Arc Intercepted by P.
    Arc ACB is The remainder of the circle.

    AB = 360 - ACB.
    (ACB-AB)/2 = P
    Substitute 360-ACB for AB
    (ACB-(360-ACB))/2 = 47
    Multiply both sides by 2:
    (ACB-(360-ACB)) = 94
    ACB-360+ACB = 94
    2ACB-360 = 94
    2ACB = 94+360 = 454
    ACB = 454/2 = 227 Deg.

    AB = 360-ACB = 360-227 = 133 Deg.

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