A 33° 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 57°.
33° is 11/120 of a full circle, or 11π/60 radians. If you face north and turn 33° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).
33° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 57° |
| Supplement (adds to 180°) | 147° |
| Explement (adds to 360°) | 327° |
| Radians | 11π/60 ≈ 0.575959 |
| Gradians | 36.6667 grad |
| Fraction of a turn | 11/120 (9.17%) |
| Degrees, minutes, seconds | 33° 0′ 0″ |
| Slope (grade) | 64.94% |
| Roof pitch | 7.79/12 |
| Compass bearing | between NNE and NE (closest to north-northeast (NNE)) |
Trigonometric values of 33°
| Function | Value |
|---|---|
| sin 33° | 0.544639 |
| cos 33° | 0.838671 |
| tan 33° | 0.649408 |
33° on a protractor
How to draw a 33° 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 33° 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 33°.
Drawing it a 33° 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 6.49 inches (about 6 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 33°, because tan 33° ≈ 0.6494.
Where you see 33° angles
- A board sloped at 33° rises about 77.9 inches over a 10-foot (120-inch) run.
- 33° of latitude on Earth spans roughly 2,279 miles north to south.
- The Earth turns 33° on its axis in about 2 h 12 min.
- Narrow acute angles like 33° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
33° angle FAQ
What type of angle is 33°?
A 33° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 33°?
The complement of 33° is 57° (together they make 90°), and the supplement is 147° (together they make 180°).
How many radians is 33 degrees?
33° = 11π/60 radians ≈ 0.576 rad. To convert degrees to radians, multiply by π/180: 33 × π/180 = 11π/60.
What is 33° as a slope or roof pitch?
33° is a 64.9% slope, which is a roof pitch of 7.79/12 (a rise of about 7 3/4 inches for every 12 inches of run).
