Hello, ^_^Engineer_Adam^_^!

Suppose that a weight is to be held 10ft below a horizontal line AB by a wire in the shape of a Y.

If the points A & B are 8ft apart, find the shortest length of wire that can be used. Code:

A 4 C 4 B
- * - - - - + - - - - *
: * | θ *
: * | *
: * | *
: * | *
10 *D
: *
: *
: *
- *W

The weight is at W. .Let __/__CBD = θ

The length of the wire is: .L .= .AD + BD + DW

In right triangle BCD, we have: .BD = 4·secθ, CD = 4·tanθ

. . So: .DW .= .10 - 4·tanθ

And we have: .L .= .2(4·secθ) + (10 - 4·tanθ) .= .8·secθ - 4·tanθ + 10

Now you can minimize L . . .