A 57° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 33° more and you get a square corner.
57° is 19/120 of a full circle, or 19π/60 radians. If you face north and turn 57° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
57° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 33° |
| Supplement (adds to 180°) | 123° |
| Explement (adds to 360°) | 303° |
| Radians | 19π/60 ≈ 0.994838 |
| Gradians | 63.3333 grad |
| Fraction of a turn | 19/120 (15.83%) |
| Degrees, minutes, seconds | 57° 0′ 0″ |
| Slope (grade) | 153.99% |
| Roof pitch | 18.48/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 57°
| Function | Value |
|---|---|
| sin 57° | 0.838671 |
| cos 57° | 0.544639 |
| tan 57° | 1.539865 |
57° on a protractor
How to draw a 57° 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 57° 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 57°.
Drawing it a 57° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.49 inches (about 6 1/2″) 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 57°, because tan 57° ≈ 1.5399.
Where you see 57° angles
- A board sloped at 57° rises about 184.8 inches over a 10-foot (120-inch) run.
- 57° of latitude on Earth spans roughly 3,936 miles north to south.
- The Earth turns 57° on its axis in about 3 h 48 min.
- Narrow acute angles like 57° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
57° angle FAQ
What type of angle is 57°?
A 57° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 57°?
The complement of 57° is 33° (together they make 90°), and the supplement is 123° (together they make 180°).
How many radians is 57 degrees?
57° = 19π/60 radians ≈ 0.9948 rad. To convert degrees to radians, multiply by π/180: 57 × π/180 = 19π/60.
What is 57° as a slope or roof pitch?
57° is a 154% slope, which is a roof pitch of 18.48/12 (a rise of about 18 1/2 inches for every 12 inches of run).
