Constructing a 30-60-90 triangle with compass and straightedge or ruler

Constructing a 30°- 60°- 90° triangle Using compass and straightedge or ruler

- Printable problem worksheet
- See all constructions

Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping. (If there is no image below, see support page.)

Step-by-step Instructions

After doing this	Your work should look like this
We start with a line segment PQ that will be the hypotenuse of the triangle..
First, we construct a 30° angle on one end of the hypotenuse. See Constructing a 30° angle.
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.
2. Draw an arc across PQ and up over above the point P. Label the point where it crosses PQ as point S.
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.
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.
5. Draw a line from P through R and continue it on beyond R to create the second side of the triangle.
Next, we construct a 60° angle on the other end of the hypotenuse. See Constructing a 60° angle.
6. Place the compass on point Q and set its width to about one third the length of the line.
7. Draw an arc across PQ and up over above the point Q. Label the point where it crosses PQ as point A.
8. With the compass on A, draw a second arc, crossing the first arc at point B
9. Draw a line from Q, through B and on to cross the line PR. Label the intersection point C.
10. Done. The triangle PQC is a 30-60-90 triangle.

Try it yourself

Click here for a printable worksheet containing 30-60-90 triangle exercises. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Constructions pages on this site

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions