At 76°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 14° more and you get a square corner.
76° is 19/90 of a full circle, or 19π/45 radians. If you face north and turn 76° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
76° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 14° |
| Supplement (adds to 180°) | 104° |
| Explement (adds to 360°) | 284° |
| Radians | 19π/45 ≈ 1.32645 |
| Gradians | 84.4444 grad |
| Fraction of a turn | 19/90 (21.11%) |
| Degrees, minutes, seconds | 76° 0′ 0″ |
| Slope (grade) | 401.08% |
| Roof pitch | 48.13/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 76°
| Function | Value |
|---|---|
| sin 76° | 0.970296 |
| cos 76° | 0.241922 |
| tan 76° | 4.010781 |
76° on a protractor
How to draw a 76° 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 76° 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 76°.
Drawing it a 76° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 2.49 inches (about 2 1/2″) 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 76°, because tan 76° ≈ 4.0108.
Where you see 76° angles
- The 4-to-1 ladder rule (1 foot out for every 4 feet up) puts a ladder at about 76° to the ground.
- 76° of latitude on Earth spans roughly 5,248 miles north to south.
- The Earth turns 76° on its axis in about 5 h 4 min.
- Narrow acute angles like 76° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
76° angle FAQ
What type of angle is 76°?
A 76° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 76°?
The complement of 76° is 14° (together they make 90°), and the supplement is 104° (together they make 180°).
How many radians is 76 degrees?
76° = 19π/45 radians ≈ 1.3265 rad. To convert degrees to radians, multiply by π/180: 76 × π/180 = 19π/45.
How do I measure a 76° angle on my screen?
Open the online protractor with 76° preset, or type 76 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
