A 78° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 12° more and you get a square corner.
78° is 13/60 of a full circle, or 13π/30 radians. The minute hand of a clock sweeps 78° in 13 minutes. If you face north and turn 78° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
78° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 12° |
| Supplement (adds to 180°) | 102° |
| Explement (adds to 360°) | 282° |
| Radians | 13π/30 ≈ 1.361357 |
| Gradians | 86.6667 grad |
| Fraction of a turn | 13/60 (21.67%) |
| Degrees, minutes, seconds | 78° 0′ 0″ |
| Slope (grade) | 470.46% |
| Roof pitch | 56.46/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 78°
| Function | Value |
|---|---|
| sin 78° | 0.978148 |
| cos 78° | 0.207912 |
| tan 78° | 4.70463 |
78° on a protractor
How to draw a 78° 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 78° 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 78°.
Drawing it a 78° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 2.13 inches (about 2 1/8″) 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 78°, because tan 78° ≈ 4.7046.
Where you see 78° angles
- 78° of latitude on Earth spans roughly 5,386 miles north to south.
- The Earth turns 78° on its axis in about 5 h 12 min.
- Narrow acute angles like 78° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
78° angle FAQ
What type of angle is 78°?
A 78° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 78°?
The complement of 78° is 12° (together they make 90°), and the supplement is 102° (together they make 180°).
How many radians is 78 degrees?
78° = 13π/30 radians ≈ 1.3614 rad. To convert degrees to radians, multiply by π/180: 78 × π/180 = 13π/30.
How do I measure a 78° angle on my screen?
Open the online protractor with 78° preset, or type 78 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
