At 64°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 26° more and you get a square corner.
64° is 8/45 of a full circle, or 16π/45 radians. If you face north and turn 64° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
64° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 26° |
| Supplement (adds to 180°) | 116° |
| Explement (adds to 360°) | 296° |
| Radians | 16π/45 ≈ 1.117011 |
| Gradians | 71.1111 grad |
| Fraction of a turn | 8/45 (17.78%) |
| Degrees, minutes, seconds | 64° 0′ 0″ |
| Slope (grade) | 205.03% |
| Roof pitch | 24.6/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 64°
| Function | Value |
|---|---|
| sin 64° | 0.898794 |
| cos 64° | 0.438371 |
| tan 64° | 2.050304 |
64° on a protractor
How to draw a 64° 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 64° 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 64°.
Drawing it a 64° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 4.88 inches (about 4 7/8″) 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 64°, because tan 64° ≈ 2.0503.
Where you see 64° angles
- A 24/12 roof pitch is 63.43°, very close to 64°.
- 64° of latitude on Earth spans roughly 4,419 miles north to south.
- The Earth turns 64° on its axis in about 4 h 16 min.
- Narrow acute angles like 64° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
64° angle FAQ
What type of angle is 64°?
A 64° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 64°?
The complement of 64° is 26° (together they make 90°), and the supplement is 116° (together they make 180°).
How many radians is 64 degrees?
64° = 16π/45 radians ≈ 1.117 rad. To convert degrees to radians, multiply by π/180: 64 × π/180 = 16π/45.
What is 64° as a slope or roof pitch?
64° is a 205% slope, which is a roof pitch of 24.6/12 (a rise of about 24 5/8 inches for every 12 inches of run).
