39 Degree Angle

A 39° angle is an acute angle: it is smaller than a right angle (90°). It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 51°.

39° is 13/120 of a full circle, or 13π/60 radians. If you face north and turn 39° clockwise, you end up facing between NNE and NE (closest to northeast (NE)).

39° angle facts

Trigonometric values of 39°

39° on a protractor

How to draw a 39° angle with a protractor

1. Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
2. Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
3. Find 39° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
4. Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 39°.

Drawing it a 39° angle without a protractor (rise and run method)

1. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
2. At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
3. Measure 8.1 inches (about 8 1/8″) up that line and make a mark.
4. Join the mark to the vertex. The angle at the vertex is 39°, because tan 39° ≈ 0.8098.

Where you see 39° angles

• A board sloped at 39° rises about 97.2 inches over a 10-foot (120-inch) run.
• 39° of latitude on Earth spans roughly 2,693 miles north to south.
• The Earth turns 39° on its axis in about 2 h 36 min.
• Narrow acute angles like 39° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.

Related angles

• Complement: 51°
• Supplement: 141°
• Explement: 321°
• Double: 78°
• 30°
• 45°
• 60°
• 90°
• 120°