A 59° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 31° more and you get a square corner.
59° is 59/360 of a full circle, or 59π/180 radians. If you face north and turn 59° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
59° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 31° |
| Supplement (adds to 180°) | 121° |
| Explement (adds to 360°) | 301° |
| Radians | 59π/180 ≈ 1.029744 |
| Gradians | 65.5556 grad |
| Fraction of a turn | 59/360 (16.39%) |
| Degrees, minutes, seconds | 59° 0′ 0″ |
| Slope (grade) | 166.43% |
| Roof pitch | 19.97/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 59°
| Function | Value |
|---|---|
| sin 59° | 0.857167 |
| cos 59° | 0.515038 |
| tan 59° | 1.664279 |
59° on a protractor
How to draw a 59° 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 59° 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 59°.
Drawing it a 59° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.01 inches (about 6″) 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 59°, because tan 59° ≈ 1.6643.
Where you see 59° angles
- A 20/12 roof pitch is 59.04°, very close to 59°.
- A board sloped at 59° rises about 199.7 inches over a 10-foot (120-inch) run.
- 59° of latitude on Earth spans roughly 4,074 miles north to south.
- The Earth turns 59° on its axis in about 3 h 56 min.
Related angles
59° angle FAQ
What type of angle is 59°?
A 59° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 59°?
The complement of 59° is 31° (together they make 90°), and the supplement is 121° (together they make 180°).
How many radians is 59 degrees?
59° = 59π/180 radians ≈ 1.0297 rad. To convert degrees to radians, multiply by π/180: 59 × π/180 = 59π/180.
What is 59° as a slope or roof pitch?
59° is a 166.4% slope, which is a roof pitch of 19.97/12 (a rise of about 20 inches for every 12 inches of run).
