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Question Number 68576 by naka3546 last updated on 13/Sep/19

Commented by naka3546 last updated on 13/Sep/19

Find  a  ,  if  [ yellow ] =  [ blue ]  Area  of  yellow  =  area  of  blue

Finda,if[yellow]=[blue]Areaofyellow=areaofblue

Answered by mr W last updated on 14/Sep/19

let R=1  (1^2 /2)[(π/2)+2a−sin ((π/2)+2a)]−(1^2 /2)((π/2)−sin (π/2))−((√2)/2)×(√2) tan a=(1/2)×(1^2 /2)((π/2)−sin (π/2))  ⇒2a−cos 2a−2 tan a=(π/4)−(3/2)  ⇒cos^2 a+tan a−a=((10−π)/8)  ⇒a≈0.4255=24.38°

letR=1122[π2+2asin(π2+2a)]122(π2sinπ2)22×2tana=12×122(π2sinπ2)2acos2a2tana=π432cos2a+tanaa=10π8a0.4255=24.38°

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