At 52°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 38° more and you get a square corner.
52° is 13/90 of a full circle, or 13π/45 radians. If you face north and turn 52° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
52° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 38° |
| Supplement (adds to 180°) | 128° |
| Explement (adds to 360°) | 308° |
| Radians | 13π/45 ≈ 0.907571 |
| Gradians | 57.7778 grad |
| Fraction of a turn | 13/90 (14.44%) |
| Degrees, minutes, seconds | 52° 0′ 0″ |
| Slope (grade) | 127.99% |
| Roof pitch | 15.36/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 52°
| Function | Value |
|---|---|
| sin 52° | 0.788011 |
| cos 52° | 0.615661 |
| tan 52° | 1.279942 |
52° on a protractor
How to draw a 52° 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 52° 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 52°.
Drawing it a 52° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7.81 inches (about 7 13/16″) 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 52°, because tan 52° ≈ 1.2799.
Where you see 52° angles
- The faces of the Great Pyramid of Giza rise at about 51.8°.
- "52/38" crown molding sits at 52° to the ceiling.
- A board sloped at 52° rises about 153.6 inches over a 10-foot (120-inch) run.
- 52° of latitude on Earth spans roughly 3,591 miles north to south.
- The Earth turns 52° on its axis in about 3 h 28 min.
Related angles
52° angle FAQ
What type of angle is 52°?
A 52° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 52°?
The complement of 52° is 38° (together they make 90°), and the supplement is 128° (together they make 180°).
How many radians is 52 degrees?
52° = 13π/45 radians ≈ 0.9076 rad. To convert degrees to radians, multiply by π/180: 52 × π/180 = 13π/45.
What is 52° as a slope or roof pitch?
52° is a 128% slope, which is a roof pitch of 15.36/12 (a rise of about 15 3/8 inches for every 12 inches of run).
