An 84° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 6° more and you get a square corner.
84° is 7/30 of a full circle, or 7π/15 radians. The minute hand of a clock sweeps 84° in 14 minutes. If you face north and turn 84° clockwise, you end up facing between ENE and E (closest to east (E)).
84° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 6° |
| Supplement (adds to 180°) | 96° |
| Explement (adds to 360°) | 276° |
| Radians | 7π/15 ≈ 1.466077 |
| Gradians | 93.3333 grad |
| Fraction of a turn | 7/30 (23.33%) |
| Degrees, minutes, seconds | 84° 0′ 0″ |
| Slope (grade) | 951.44% |
| Roof pitch | 114.17/12 |
| Compass bearing | between ENE and E (closest to east (E)) |
Trigonometric values of 84°
| Function | Value |
|---|---|
| sin 84° | 0.994522 |
| cos 84° | 0.104528 |
| tan 84° | 9.514364 |
84° on a protractor
How to draw an 84° 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 84° 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 84°.
Drawing it an 84° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 1.05 inches (about 1 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 84°, because tan 84° ≈ 9.5144.
Where you see 84° angles
- 84° of latitude on Earth spans roughly 5,800 miles north to south.
- The Earth turns 84° on its axis in about 5 h 36 min.
- Narrow acute angles like 84° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
84° angle FAQ
What type of angle is 84°?
An 84° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 84°?
The complement of 84° is 6° (together they make 90°), and the supplement is 96° (together they make 180°).
How many radians is 84 degrees?
84° = 7π/15 radians ≈ 1.4661 rad. To convert degrees to radians, multiply by π/180: 84 × π/180 = 7π/15.
How do I measure an 84° angle on my screen?
Open the online protractor with 84° preset, or type 84 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
