Three lengths, one triangle
A shop cuts three metal strips for a shelf bracket. The shop measures no angle.
Step 1 of 3
- A base. Two corners are fixed.
- An arc from the other end. It closes.
- Arcs too short for the base. Together they are shorter than it. They never meet.
Base, arc, arc, join
Rule one length as the base. Set the span to the second length. Strike an arc from one end. Set the span to the third length. Strike an arc from the other end.
The arcs cross at the third corner. Join that corner to both ends of the base. The triangle closes when its three sides join.
Each length must be less than the other two added together. Then the arcs cross.
Only the longest length can fail. Add the two shorter lengths. Compare the sum with the longest. 3 + 4 = 7, which is more than 5. So 3, 4 and 5 close. 3 + 4 = 7, which is less than 9. So 3, 4 and 9 do not close.
Slide the third length. Watch whether the arcs cross.
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