At 10°, this angle is acute, meaning it is narrower than the corner of a square. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 80°.
10° is one thirty-sixth (1/36) of a full circle, or π/18 radians. If you face north and turn 10° clockwise, you end up facing between N and NNE (closest to north (N)).
10° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 80° |
| Supplement (adds to 180°) | 170° |
| Explement (adds to 360°) | 350° |
| Radians | π/18 ≈ 0.174533 |
| Gradians | 11.1111 grad |
| Fraction of a turn | one thirty-sixth (1/36) (2.78%) |
| Degrees, minutes, seconds | 10° 0′ 0″ |
| Slope (grade) | 17.63% |
| Roof pitch | 2.12/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 10°
| Function | Value |
|---|---|
| sin 10° | 0.173648 |
| cos 10° | 0.984808 |
| tan 10° | 0.176327 |
10° on a protractor
How to draw a 10° 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 10° 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 10°.
Drawing it a 10° 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 1.76 inches (about 1 3/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 10°, because tan 10° ≈ 0.1763.
Where you see 10° angles
- Typical golf driver lofts run from about 9° to 12°.
- Divide a circle into 36 equal slices and each slice is 10°, e.g. 36 spokes on a wheel or 36 equal pie-chart wedges.
- A 18-sided frame (18-sided polygon) is assembled with 10° miter cuts.
- A 2/12 roof pitch is 9.46°, very close to 10°.
- A board sloped at 10° rises about 21.2 inches over a 10-foot (120-inch) run.
- 10° of latitude on Earth spans roughly 691 miles north to south.
- The Earth turns 10° on its axis in about 40 minutes.
Related angles
10° angle FAQ
What type of angle is 10°?
A 10° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 10°?
The complement of 10° is 80° (together they make 90°), and the supplement is 170° (together they make 180°).
How many radians is 10 degrees?
10° = π/18 radians ≈ 0.1745 rad. To convert degrees to radians, multiply by π/180: 10 × π/180 = π/18.
What is 10° as a slope or roof pitch?
10° is a 17.6% slope, which is a roof pitch of 2.12/12 (a rise of about 2 1/8 inches for every 12 inches of run).
