Start with two line segments and the included angle.


1. Mark a point A that will be one vertex of the new triangle. 

2. Draw a ray from point A.
This will become the side AB of the new triangle, so make it longer than AB. 

3. Set the compasses' width to the length of the given side AB. 

4. Set the compasses on A, and mark a point B on the ray just drawn. 

5. With the compasses set to any convenient width, from the point A on the given angle,
draw an arc across both lines.. 

6. Without changing the compasses' width, draw a similar sized arc at point A on the new triangle. 

7. Set the compasses to the arc width at the given angle A.
This the distance between the points where the arc intersects the sides of the angle. 

8. Make a similar arc on the new triangle so it crosses the previous arc. 

9. Draw a ray from A, through where the arcs intersect and onwards.
This will become side AC of the triangle so make it longer than AC. 

10. Set the compasses' width to the distance AC. 

11. With the compasses on A, make an arc across the second ray, creating point C. 

12. Draw the line BC, the third side of the triangle 

Done, the triangle ABC has the desired two side lengths and included angle. 
