At 67°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 23° more and you get a square corner.
67° is 67/360 of a full circle, or 67π/180 radians. If you face north and turn 67° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
67° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 23° |
| Supplement (adds to 180°) | 113° |
| Explement (adds to 360°) | 293° |
| Radians | 67π/180 ≈ 1.169371 |
| Gradians | 74.4444 grad |
| Fraction of a turn | 67/360 (18.61%) |
| Degrees, minutes, seconds | 67° 0′ 0″ |
| Slope (grade) | 235.59% |
| Roof pitch | 28.27/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 67°
| Function | Value |
|---|---|
| sin 67° | 0.920505 |
| cos 67° | 0.390731 |
| tan 67° | 2.355852 |
67° on a protractor
How to draw a 67° 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 67° 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 67°.
Drawing it a 67° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 4.24 inches (about 4 1/4″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 67°, because tan 67° ≈ 2.3559.
Where you see 67° angles
- 67° of latitude on Earth spans roughly 4,626 miles north to south.
- The Earth turns 67° on its axis in about 4 h 28 min.
- Narrow acute angles like 67° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
67° angle FAQ
What type of angle is 67°?
A 67° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 67°?
The complement of 67° is 23° (together they make 90°), and the supplement is 113° (together they make 180°).
How many radians is 67 degrees?
67° = 67π/180 radians ≈ 1.1694 rad. To convert degrees to radians, multiply by π/180: 67 × π/180 = 67π/180.
What is 67° as a slope or roof pitch?
67° is a 235.6% slope, which is a roof pitch of 28.27/12 (a rise of about 28 1/4 inches for every 12 inches of run).
