A 56° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 34° more and you get a square corner.
56° is 7/45 of a full circle, or 14π/45 radians. If you face north and turn 56° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
56° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 34° |
| Supplement (adds to 180°) | 124° |
| Explement (adds to 360°) | 304° |
| Radians | 14π/45 ≈ 0.977384 |
| Gradians | 62.2222 grad |
| Fraction of a turn | 7/45 (15.56%) |
| Degrees, minutes, seconds | 56° 0′ 0″ |
| Slope (grade) | 148.26% |
| Roof pitch | 17.79/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 56°
| Function | Value |
|---|---|
| sin 56° | 0.829038 |
| cos 56° | 0.559193 |
| tan 56° | 1.482561 |
56° on a protractor
How to draw a 56° 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 56° 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 56°.
Drawing it a 56° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.75 inches (about 6 3/4″) 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 56°, because tan 56° ≈ 1.4826.
Where you see 56° angles
- Sand wedges typically have between 54° and 58° of loft; 56° is the most common.
- A 18/12 roof pitch is 56.31°, very close to 56°.
- A board sloped at 56° rises about 177.9 inches over a 10-foot (120-inch) run.
- 56° of latitude on Earth spans roughly 3,867 miles north to south.
- The Earth turns 56° on its axis in about 3 h 44 min.
Related angles
56° angle FAQ
What type of angle is 56°?
A 56° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 56°?
The complement of 56° is 34° (together they make 90°), and the supplement is 124° (together they make 180°).
How many radians is 56 degrees?
56° = 14π/45 radians ≈ 0.9774 rad. To convert degrees to radians, multiply by π/180: 56 × π/180 = 14π/45.
What is 56° as a slope or roof pitch?
56° is a 148.3% slope, which is a roof pitch of 17.79/12 (a rise of about 17 3/4 inches for every 12 inches of run).
