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Topic: help
Replies: 1   Last Post: Jan 17, 2008 8:26 AM

 Messages: [ Previous | Next ]
 Pavel314 Posts: 75 Registered: 7/2/05
Re: help
Posted: Jan 17, 2008 8:26 AM

"Tony Welscher" <389removethisnow@insightbb.com> wrote in message
news:XeGdnVr26tL0MXXYnZ2dnUVZ_oytnZ2d@insightbb.com...
>
> First let me say that if this is too simple for this site I am sorry. I'm
> just a old timer that is trying to maximize my cuts on a sheet of
> plywood.
>
> Trapezoid Question
> I know the base measurement and the angles of the trapezoid.
> I need the sides and the top to be equal
> Is there a formula that I can input the base length and angles to find the
> 3 equal sides?
>
> The reverse to this question
> I know the equal length of the 2 sides and the top. I know the degrees of
> the angles
> Is there a formula that will tell what the base needs to be.
>
>
> --
> Tony Welscher

Solving the reverse question is easier. If you drop perpendiculars from the
ends of the top to the base, you end up with a rectangle with a triangle on
each side. Let S be the length of your sides and top. The length of the side
of one triangle (T) which is on the base (B) of the trapezoid would be:

T = S * sin(A - 90)

Since B = S + 2 * T,

B = S + 2 * S * sin(A - 90)

To solve the first question, solve the equation for S.

B = S * ( 1 + 2 * sin (A - 90))

S = B / ( 1 + 2 * sin(A - 90))

Paul

Date Subject Author
3/5/07 Tony Welscher
1/17/08 Pavel314