A 36° 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 54°.
36° is one tenth (1/10) of a full circle, or π/5 radians. The minute hand of a clock sweeps 36° in 6 minutes. If you face north and turn 36° clockwise, you end up facing between NNE and NE (closest to northeast (NE)).
36° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 54° |
| Supplement (adds to 180°) | 144° |
| Explement (adds to 360°) | 324° |
| Radians | π/5 ≈ 0.628319 |
| Gradians | 40 grad |
| Fraction of a turn | one tenth (1/10) (10%) |
| Degrees, minutes, seconds | 36° 0′ 0″ |
| Slope (grade) | 72.65% |
| Roof pitch | 8.72/12 |
| Compass bearing | between NNE and NE (closest to northeast (NE)) |
Trigonometric values of 36°
| Function | Value |
|---|---|
| sin 36° | √(10 − 2√5)/4 ≈ 0.587785 |
| cos 36° | (√5 + 1)/4 ≈ 0.809017 |
| tan 36° | 0.726543 |
36° on a protractor
How to draw a 36° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 36° 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.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 36°.
Drawing it a 36° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- 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).
- Measure 7.27 inches (about 7 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 36°, because tan 36° ≈ 0.7265.
Where you see 36° angles
- Each point of a regular five-pointed star measures 36°.
- A five-sided (pentagon) frame uses 36° miters.
- Divide a circle into 10 equal slices and each slice is 36°, e.g. 10 spokes on a wheel or 10 equal pie-chart wedges.
- A board sloped at 36° rises about 87.2 inches over a 10-foot (120-inch) run.
- 36° of latitude on Earth spans roughly 2,486 miles north to south.
- The Earth turns 36° on its axis in about 2 h 24 min.
Related angles
36° angle FAQ
What type of angle is 36°?
A 36° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 36°?
The complement of 36° is 54° (together they make 90°), and the supplement is 144° (together they make 180°).
How many radians is 36 degrees?
36° = π/5 radians ≈ 0.6283 rad. To convert degrees to radians, multiply by π/180: 36 × π/180 = π/5.
What is 36° as a slope or roof pitch?
36° is a 72.7% slope, which is a roof pitch of 8.72/12 (a rise of about 8 3/4 inches for every 12 inches of run).
