Given three line segments, L1,L2,L3, construct a triangle if possible by defining the coordinates of the three corners.



Here's the math to determine the coordinates of the third point if the line labeled L1 (and with length L1) is placed horizontally starting at coordinates (0,0).

1. L22 = s2 + a2                                         (Pythagoras)
2. L32 = (L1-s)2 + a2                               (Pythagoras)
3. L22 - s2 = L32 -(L1- s)2                        (Identity - solve 1 & 2 for a2)
4. L22 - s2 = L32 - L12 + 2*L1*s - s2      (Expand 3.)
5. s = ( L22 + L12 - L32) / (2*L1)            (Solve 4. for "s")
6. a = sqrt( L22 - s2 )                                 (Solve 1. for "a")

The program lets you view the effect of changing side lengths by drawing the resulting triangle and displaying the (s, a) coordinate.

Running/Exploring the Program