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Question Number 186721 by Mingma last updated on 09/Feb/23

Commented by Mingma last updated on 09/Feb/23

How far is the arc from A to B? The side of the square is 2 in length

Answered by HeferH last updated on 09/Feb/23

Commented by HeferH last updated on 09/Feb/23

1−a^2 = (2 + (√2) + a)(2−(√2)−a) 1−a^2 = [2 + ((√2) + a)][2 −((√2)+a)] 1−a^2 = 4 − ((√2) + a)^2 1 − a^2 = 4 −(2 + a^2 + 2a(√2)) 1 − a^2 = 2 − a^2 − 2a(√2) −1 = −2a(√2) a = (1/(2(√2))) = ((√2)/4) ⇒ 2 − (√2) − ((√2)/4) = 2 − ((5(√2))/4) = ((8 − 5(√2))/4)

1−a2=(2+2+a)(2−2−a)1−a2=[2+(2+a)][2−(2+a)]1−a2=4−(2+a)21−a2=4−(2+a2+2a2)1−a2=2−a2−2a2−1=−2a2a=122=24⇒2−2−24=2−524=8−524

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