A 51° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 39° more and you get a square corner.
51° is 17/120 of a full circle, or 17π/60 radians. If you face north and turn 51° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
51° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 39° |
| Supplement (adds to 180°) | 129° |
| Explement (adds to 360°) | 309° |
| Radians | 17π/60 ≈ 0.890118 |
| Gradians | 56.6667 grad |
| Fraction of a turn | 17/120 (14.17%) |
| Degrees, minutes, seconds | 51° 0′ 0″ |
| Slope (grade) | 123.49% |
| Roof pitch | 14.82/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 51°
| Function | Value |
|---|---|
| sin 51° | 0.777146 |
| cos 51° | 0.62932 |
| tan 51° | 1.234897 |
51° on a protractor
How to draw a 51° 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 51° 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 51°.
Drawing it a 51° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 8.1 inches (about 8 1/8″) 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 51°, because tan 51° ≈ 1.2349.
Where you see 51° angles
- A 15/12 roof pitch is 51.34°, very close to 51°.
- A board sloped at 51° rises about 148.2 inches over a 10-foot (120-inch) run.
- 51° of latitude on Earth spans roughly 3,522 miles north to south.
- The Earth turns 51° on its axis in about 3 h 24 min.
Related angles
51° angle FAQ
What type of angle is 51°?
A 51° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 51°?
The complement of 51° is 39° (together they make 90°), and the supplement is 129° (together they make 180°).
How many radians is 51 degrees?
51° = 17π/60 radians ≈ 0.8901 rad. To convert degrees to radians, multiply by π/180: 51 × π/180 = 17π/60.
What is 51° as a slope or roof pitch?
51° is a 123.5% slope, which is a roof pitch of 14.82/12 (a rise of about 14 7/8 inches for every 12 inches of run).
