A 77° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 13° more and you get a square corner.
77° is 77/360 of a full circle, or 77π/180 radians. If you face north and turn 77° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
77° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 13° |
| Supplement (adds to 180°) | 103° |
| Explement (adds to 360°) | 283° |
| Radians | 77π/180 ≈ 1.343904 |
| Gradians | 85.5556 grad |
| Fraction of a turn | 77/360 (21.39%) |
| Degrees, minutes, seconds | 77° 0′ 0″ |
| Slope (grade) | 433.15% |
| Roof pitch | 51.98/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 77°
| Function | Value |
|---|---|
| sin 77° | 0.97437 |
| cos 77° | 0.224951 |
| tan 77° | 4.331476 |
77° on a protractor
How to draw a 77° 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 77° 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 77°.
Drawing it a 77° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 2.31 inches (about 2 5/16″) 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 77°, because tan 77° ≈ 4.3315.
Where you see 77° angles
- 77° of latitude on Earth spans roughly 5,317 miles north to south.
- The Earth turns 77° on its axis in about 5 h 8 min.
- Narrow acute angles like 77° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
77° angle FAQ
What type of angle is 77°?
A 77° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 77°?
The complement of 77° is 13° (together they make 90°), and the supplement is 103° (together they make 180°).
How many radians is 77 degrees?
77° = 77π/180 radians ≈ 1.3439 rad. To convert degrees to radians, multiply by π/180: 77 × π/180 = 77π/180.
How do I measure a 77° angle on my screen?
Open the online protractor with 77° preset, or type 77 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
