Lesson 10 of 17
60°, 30° and 15° with a compass
Show on a big screenA set square has a 60° corner and a 30° corner. A compass can draw both.
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Step 1 of 4
- A ray OP, and an arc about O through P.
- The same span from P cuts the arc at C.
- Rule OC. Triangle OPC has three equal sides.
- Bisect the corner at O. It splits into 30° and 30°.
The rule
Two arcs of one span make an equilateral triangle. Its corner is 60°. Bisect a corner to halve it. Bisect 60° to get 30°. Bisect 30° to get 15°.
Why 60°? In triangle OPC, OP and OC are both radii of that arc. A radius joins the centre to the arc. PC has the same span. So all three sides are equal: OP = OC = PC. A triangle like that is equilateral. Its three angles are equal, and they add to 180°. Each is 180 ÷ 3 = 60°.
To add 60°, strike the same span. Start where the last ray cuts the arc. The new ray is 60° further round.
Example: bisect twice to get 15°. Add 60° to that for 75°. Bisect 60° once, then add 60°, for 90°.
Try the lab to finish this lesson.