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Math Help - finding the shaded area of a triangle

  1. #1
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    finding the shaded area of a triangle

    i need help with this problem. i have absolutely no clue how to solve it.

    Consider the shaded region outside the sector of the circle of radius 8 meters and inside the right triangle. write the area A of the region as a function of Θ.

    Please and Thank you!
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  2. #2
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    Quote Originally Posted by luckystar001 View Post
    i need help with this problem. i have absolutely no clue how to solve it.

    Consider the shaded region outside the sector of the circle of radius 8 meters and inside the right triangle. write the area A of the region as a function of Θ.

    Please and Thank you!
    Hi luckystar001,

    the shaded region is the difference between the triangle area and a sector of a circle.
    Hence the shaded region is

    triangle\ area-sector\ area.

    The triangle area is 0.5(base)(height)

    but since tan\theta=\frac{height}{8}

    \Rightarrow\ h=8tan\theta\ \Rightarrow\ triangle\ area=0.5(8)(8tan\theta)


    The area of the complete circle is {\pi}r^2={\pi}8^2

    The area of the sector is a fraction of the area of the full circle.

    That fraction is \frac{\theta}{360^o}

    Can you complete?
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  3. #3
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    Thank you very much! I wouldn't have thought of that. You're a genius!
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