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First, we construct a 30° angle on one end of the hypotenuse. See
Constructing a 30° angle. |
| Step 1 |
Starting with the hypotenuse line PQ, set the compass on P,
and set its width to about one third the length of the line. |
| Step 2 |
Draw an arc across PQ and up over above the point P. Label the point where it crosses PQ as point S. |
| Step 3 |
Without changing the compass width, move the compass to the point S.
Draw a broad arc that crosses the first one and goes well to the right.
Label the point where the two arcs cross as point T. |
| Step 4 |
Again without changing the compass width, move the compass to the point T, and draw an arc across the previous arc,
creating point R. |
| Step 5 |
Draw a line from P through R and continue it on beyond R to create the second side of the triangle. |
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Next, we construct a 60° angle on the other end of the hypotenuse. See
Constructing a 60° angle. |
| Step 6 |
Place the compass on point Q and set its width to about one third the length of the line. |
| Step 7 |
Draw an arc across PQ and up over above the point Q. Label the point where it crosses PQ as point A. |
| Step 8 |
With the compass on A, draw a second arc, crossing the first arc at point B |
| Step 9 |
Draw a line from Q, through B and on to cross the line PR. Label the intersection point C. |
| Step 10 |
Done. The triangle PQC is a 30-60-90 triangle. |
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