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  A rectangle is inscribed in a smicircle of radius r. A straight line from the center...

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sara212 | Student, Undergraduate | Salutatorian

Posted July 11, 2013 at 3:10 PM via web

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A rectangle is inscribed in a smicircle of radius r. A straight line from the center of circle to the point where vertex of the ractangle meets the circle, forms an angle `theta`

Find the expression for the area of ractanglein term of r and a sine function. Find the area of circle if r=5 cm and `theta` = `26^(o)`

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 11, 2013 at 3:20 PM (Answer #1)

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A rectangle is inscribed in a semicircle of radius r. A straight line from the center of circle to the point where vertex of the rectangle meets the circle, forms an angle `theta` .

If the radius of the circle is r, the sides of the rectangle are `r*sin theta` and `2*r*cos theta` . The area of the rectangle in terms of r and a sine function is A = `2*r*cos theta*r*sin theta `

= `2*r^2*sin theta*sqrt(1 - sin^2 theta)`

If r = 5 and `theta` = 26 degrees, the area of the rectangle is `2*25*sin 26*sqrt(1 - sin^2 26)` = 19.7 cm^2

For the given radius and value of `theta` the area of the rectangle is 19.7 cm^2

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