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The area of an equilateral triangle MNO is 10 cm². (See diagram below)  Find the length of the arc L if angle β = 111°.

 

 Feb 14, 2020
edited by Dragan  Feb 14, 2020
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The side of the equilateral triangle, S,   will   =   the radius of the  circle

 

Area of equilateral  triangle  = (sqrt(3) /4) S^2

 

10  = (sqrt (3) / 4 ) * S^2

 

10 * 4  /sqrt (3)  =  S^2

 

40 / sqrt (3)  = S^2       take the square  root  of both sides

 

S =  sqrt (40) / (3)^(1/4)  = S =  circle radius

 

arc length =  2pi  * R *  [ central angle measure /  360)  =      2pi * [ sqrt (40 / 3^(1/4) ]   (111/ 360 ) ≈    9.31 cm

 

 

cool cool cool

 Feb 14, 2020

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