# L=3/sinΘcos²Θ - Proving the equation

by Andrew
(New York)

The lower right-hand corner of a long piece of rectangular paper 6 in. wide is folded over to the left-hand edge as shown. The length L of the fold
depends on the angle (Theta). Show that: (refer to equation above.)

### Comments for L=3/sinΘcos²Θ - Proving the equation

 Apr 16, 2012 L=3/sinΘcos²Θ - Proving the equation by: Staff Question: by Andrew (New York) The lower right-hand corner of a long piece of rectangular paper 6 in. wide is folded over to the left-hand edge as shown. The length L of the fold depends on the angle (Theta). Show that: (refer to equation above.) Answer: Refer to the following diagram: (1) If your browser is Firefox, click the following link to VIEW the solution; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter: Use the Backspace key to return to this page http://www.solving-math-problems.com/images/triangle-diagram-2012-04-16-01.png AB ∥DE AB = 6 △CAD ≅ △EAD ∠CAD = ∠EAD = Θ ∠BAC = 90° - 2Θ cos(90°-2Θ) = AB/AC = 6/AC cos(90°-2Θ) = sin(2Θ) = 6/AC sin(2Θ) = 6/AC AC = 6/sin(2Θ) cos(Θ) = AC/L L = AC/cos(Θ) L = [6/sin(2Θ)]/cos(Θ) L = 6/[sin(2Θ)*cos(Θ)] sin(2Θ) = Sin (Θ + Θ) = Sin(Θ)Cos(Θ) + Cos (Θ)Sin(Θ)= 2 Sin(Θ)Cos(Θ) sin(2Θ) = 2*sin(Θ)*cos(Θ) L = 6/[2*sin(Θ)*cos(Θ)*cos(Θ)] L = 3/[sin(Θ)*cos²(Θ)] Thanks for writing. Staff www.solving-math-problems.com