At 58°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 32° more and you get a square corner.
58° is 29/180 of a full circle, or 29π/90 radians. If you face north and turn 58° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
58° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 32° |
| Supplement (adds to 180°) | 122° |
| Explement (adds to 360°) | 302° |
| Radians | 29π/90 ≈ 1.012291 |
| Gradians | 64.4444 grad |
| Fraction of a turn | 29/180 (16.11%) |
| Degrees, minutes, seconds | 58° 0′ 0″ |
| Slope (grade) | 160.03% |
| Roof pitch | 19.2/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 58°
| Function | Value |
|---|---|
| sin 58° | 0.848048 |
| cos 58° | 0.529919 |
| tan 58° | 1.600335 |
58° on a protractor
How to draw a 58° 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 58° 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 58°.
Drawing it a 58° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.25 inches (about 6 1/4″) 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 58°, because tan 58° ≈ 1.6003.
Where you see 58° angles
- A 19/12 roof pitch is 57.72°, very close to 58°.
- A board sloped at 58° rises about 192 inches over a 10-foot (120-inch) run.
- 58° of latitude on Earth spans roughly 4,005 miles north to south.
- The Earth turns 58° on its axis in about 3 h 52 min.
Related angles
58° angle FAQ
What type of angle is 58°?
A 58° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 58°?
The complement of 58° is 32° (together they make 90°), and the supplement is 122° (together they make 180°).
How many radians is 58 degrees?
58° = 29π/90 radians ≈ 1.0123 rad. To convert degrees to radians, multiply by π/180: 58 × π/180 = 29π/90.
What is 58° as a slope or roof pitch?
58° is a 160% slope, which is a roof pitch of 19.2/12 (a rise of about 19 1/4 inches for every 12 inches of run).
