An 11° angle is classed as acute because it measures less than 90°. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 79°.
11° is 11/360 of a full circle, or 11π/180 radians. If you face north and turn 11° clockwise, you end up facing between N and NNE (closest to north (N)).
11° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 79° |
| Supplement (adds to 180°) | 169° |
| Explement (adds to 360°) | 349° |
| Radians | 11π/180 ≈ 0.191986 |
| Gradians | 12.2222 grad |
| Fraction of a turn | 11/360 (3.06%) |
| Degrees, minutes, seconds | 11° 0′ 0″ |
| Slope (grade) | 19.44% |
| Roof pitch | 2.33/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 11°
| Function | Value |
|---|---|
| sin 11° | 0.190809 |
| cos 11° | 0.981627 |
| tan 11° | 0.19438 |
11° on a protractor
How to draw an 11° 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 11° 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 11°.
Drawing it an 11° 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 1.94 inches (about 1 15/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 11°, because tan 11° ≈ 0.1944.
Where you see 11° angles
- A board sloped at 11° rises about 23.3 inches over a 10-foot (120-inch) run.
- 11° of latitude on Earth spans roughly 760 miles north to south.
- The Earth turns 11° on its axis in about 44 minutes.
- Narrow acute angles like 11° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
11° angle FAQ
What type of angle is 11°?
An 11° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 11°?
The complement of 11° is 79° (together they make 90°), and the supplement is 169° (together they make 180°).
How many radians is 11 degrees?
11° = 11π/180 radians ≈ 0.192 rad. To convert degrees to radians, multiply by π/180: 11 × π/180 = 11π/180.
What is 11° as a slope or roof pitch?
11° is a 19.4% slope, which is a roof pitch of 2.33/12 (a rise of about 2 3/8 inches for every 12 inches of run).
