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Math Help - Please help! (Area)

  1. #1
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    Question Please help! (Area)

    A central angle of a circle with radius 10 has a measure of 1.35 radians. The secant line between the end points of the arc of the angle divides the sector swept by the arc into two regions, one a triangle and the other bounded by the secant and the arc. What is the area of the region bounded by the secant and the arc?

    This is what I have so far:
    A1=1/2*r squared*theta, so A1=1/2*10 squared*1.35 rad=67.5

    A2=1/2*a*b*sin theta, so A2=1/2*10*?*sin ?

    A=A1-A2, so 67.5-??


    *I'm not sure how to find b or how about sin theta in A2.... ?

    (My scanner isn't working properly so I drew the picture that correlates to the problem below)


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  3. #3
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    Quote Originally Posted by accordry View Post
    A central angle of a circle with radius 10 has a measure of 1.35 radians. The secant line between the end points of the arc of the angle divides the sector swept by the arc into two regions, one a triangle and the other bounded by the secant and the arc. What is the area of the region bounded by the secant and the arc?

    This is what I have so far:
    A1=1/2*r squared*theta, so A1=1/2*10 squared*1.35 rad=67.5

    A2=1/2*a*b*sin theta, so A2=1/2*10*?*sin ?

    A=A1-A2, so 67.5-??


    *I'm not sure how to find b or how about sin theta in A2.... ?
    Your A1 is the area of the sector.

    Your A2 is the area of the isosceles tiangle, where your a and b are radii of the circle, and theta is the included angle between a and b ....or the given central angle 1.35 radians, so,
    A2 = (1/2)(10)(10)sin(1.35 rad) = 48.786 sq.units

    Hence, area of circular segment is
    A = 67.5 - 48.786 = 18.714 sq.units ----answer.
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