A 68° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 22° more and you get a square corner.
68° is 17/90 of a full circle, or 17π/45 radians. If you face north and turn 68° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
68° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 22° |
| Supplement (adds to 180°) | 112° |
| Explement (adds to 360°) | 292° |
| Radians | 17π/45 ≈ 1.186824 |
| Gradians | 75.5556 grad |
| Fraction of a turn | 17/90 (18.89%) |
| Degrees, minutes, seconds | 68° 0′ 0″ |
| Slope (grade) | 247.51% |
| Roof pitch | 29.7/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 68°
| Function | Value |
|---|---|
| sin 68° | 0.927184 |
| cos 68° | 0.374607 |
| tan 68° | 2.475087 |
68° on a protractor
How to draw a 68° 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 68° 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 68°.
Drawing it a 68° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 4.04 inches (about 4 1/16″) 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 68°, because tan 68° ≈ 2.4751.
Where you see 68° angles
- 68° of latitude on Earth spans roughly 4,695 miles north to south.
- The Earth turns 68° on its axis in about 4 h 32 min.
- Narrow acute angles like 68° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
68° angle FAQ
What type of angle is 68°?
A 68° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 68°?
The complement of 68° is 22° (together they make 90°), and the supplement is 112° (together they make 180°).
How many radians is 68 degrees?
68° = 17π/45 radians ≈ 1.1868 rad. To convert degrees to radians, multiply by π/180: 68 × π/180 = 17π/45.
What is 68° as a slope or roof pitch?
68° is a 247.5% slope, which is a roof pitch of 29.7/12 (a rise of about 29 3/4 inches for every 12 inches of run).
