A 27° 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 63°.
27° is 3/40 of a full circle, or 3π/20 radians. If you face north and turn 27° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).
27° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 63° |
| Supplement (adds to 180°) | 153° |
| Explement (adds to 360°) | 333° |
| Radians | 3π/20 ≈ 0.471239 |
| Gradians | 30 grad |
| Fraction of a turn | 3/40 (7.5%) |
| Degrees, minutes, seconds | 27° 0′ 0″ |
| Slope (grade) | 50.95% |
| Roof pitch | 6.11/12 |
| Compass bearing | between NNE and NE (closest to north-northeast (NNE)) |
Trigonometric values of 27°
| Function | Value |
|---|---|
| sin 27° | 0.45399 |
| cos 27° | 0.891007 |
| tan 27° | 0.509525 |
27° on a protractor
How to draw a 27° 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 27° 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 27°.
Drawing it a 27° 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 5.1 inches (about 5 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 27°, because tan 27° ≈ 0.5095.
Where you see 27° angles
- A 6/12 roof pitch is 26.57°, very close to 27°.
- A board sloped at 27° rises about 61.1 inches over a 10-foot (120-inch) run.
- 27° of latitude on Earth spans roughly 1,864 miles north to south.
- The Earth turns 27° on its axis in about 1 h 48 min.
Related angles
27° angle FAQ
What type of angle is 27°?
A 27° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 27°?
The complement of 27° is 63° (together they make 90°), and the supplement is 153° (together they make 180°).
How many radians is 27 degrees?
27° = 3π/20 radians ≈ 0.4712 rad. To convert degrees to radians, multiply by π/180: 27 × π/180 = 3π/20.
What is 27° as a slope or roof pitch?
27° is a 51% slope, which is a roof pitch of 6.11/12 (a rise of about 6 1/8 inches for every 12 inches of run).
