A 66° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 24° more and you get a square corner.
66° is 11/60 of a full circle, or 11π/30 radians. The minute hand of a clock sweeps 66° in 11 minutes. If you face north and turn 66° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
66° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 24° |
| Supplement (adds to 180°) | 114° |
| Explement (adds to 360°) | 294° |
| Radians | 11π/30 ≈ 1.151917 |
| Gradians | 73.3333 grad |
| Fraction of a turn | 11/60 (18.33%) |
| Degrees, minutes, seconds | 66° 0′ 0″ |
| Slope (grade) | 224.6% |
| Roof pitch | 26.95/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 66°
| Function | Value |
|---|---|
| sin 66° | 0.913545 |
| cos 66° | 0.406737 |
| tan 66° | 2.246037 |
66° on a protractor
How to draw a 66° 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 66° 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 66°.
Drawing it a 66° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 4.45 inches (about 4 7/16″) 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 66°, because tan 66° ≈ 2.246.
Where you see 66° angles
- 66° of latitude on Earth spans roughly 4,557 miles north to south.
- The Earth turns 66° on its axis in about 4 h 24 min.
- Narrow acute angles like 66° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
66° angle FAQ
What type of angle is 66°?
A 66° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 66°?
The complement of 66° is 24° (together they make 90°), and the supplement is 114° (together they make 180°).
How many radians is 66 degrees?
66° = 11π/30 radians ≈ 1.1519 rad. To convert degrees to radians, multiply by π/180: 66 × π/180 = 11π/30.
What is 66° as a slope or roof pitch?
66° is a 224.6% slope, which is a roof pitch of 26.95/12 (a rise of about 27 inches for every 12 inches of run).
