At 82°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 8° more and you get a square corner.
82° is 41/180 of a full circle, or 41π/90 radians. If you face north and turn 82° clockwise, you end up facing between ENE and E (closest to east (E)).
82° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 8° |
| Supplement (adds to 180°) | 98° |
| Explement (adds to 360°) | 278° |
| Radians | 41π/90 ≈ 1.43117 |
| Gradians | 91.1111 grad |
| Fraction of a turn | 41/180 (22.78%) |
| Degrees, minutes, seconds | 82° 0′ 0″ |
| Slope (grade) | 711.54% |
| Roof pitch | 85.38/12 |
| Compass bearing | between ENE and E (closest to east (E)) |
Trigonometric values of 82°
| Function | Value |
|---|---|
| sin 82° | 0.990268 |
| cos 82° | 0.139173 |
| tan 82° | 7.11537 |
82° on a protractor
How to draw an 82° 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 82° 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 82°.
Drawing it an 82° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 1.41 inches (about 1 3/8″) 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 82°, because tan 82° ≈ 7.1154.
Where you see 82° angles
- Flat-head wood and machine screws in the US use an 82° countersink.
- 82° of latitude on Earth spans roughly 5,662 miles north to south.
- The Earth turns 82° on its axis in about 5 h 28 min.
- Narrow acute angles like 82° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
82° angle FAQ
What type of angle is 82°?
An 82° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 82°?
The complement of 82° is 8° (together they make 90°), and the supplement is 98° (together they make 180°).
How many radians is 82 degrees?
82° = 41π/90 radians ≈ 1.4312 rad. To convert degrees to radians, multiply by π/180: 82 × π/180 = 41π/90.
How do I measure an 82° angle on my screen?
Open the online protractor with 82° preset, or type 82 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
