Geometric Ratio Pipe Problem: How to Find D2/D1?

xzibition8612
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Homework Statement



Find D2/D1.
See attachment.

Homework Equations





The Attempt at a Solution


Ans: D2/D1 = 0.68

I can't figure this one out. Any special trigonometric identities that might help here? Thanks.
 

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Draw two more lines to/from the point where the upper diagonal line intersects the lower horisontal line. One of them should be vertical. The other perpendicular to the diagonal lines. Now you have a rectangle and a bunch of right triangles to work with. Figure out all the other angles and draw them into your diagram.

One of the right triangles will have an edge of length D2. Use that to find the lengths of the other sides in units of D2. Keep doing that sort of thing until you have the length of D1 in units of D2.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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