A 75° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 15° more and you get a square corner.
75° is 5/24 of a full circle, or 5π/12 radians. If you face north and turn 75° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
75° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 15° |
| Supplement (adds to 180°) | 105° |
| Explement (adds to 360°) | 285° |
| Radians | 5π/12 ≈ 1.308997 |
| Gradians | 83.3333 grad |
| Fraction of a turn | 5/24 (20.83%) |
| Degrees, minutes, seconds | 75° 0′ 0″ |
| Slope (grade) | 373.21% |
| Roof pitch | 44.78/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 75°
| Function | Value |
|---|---|
| sin 75° | (√6 + √2)/4 ≈ 0.965926 |
| cos 75° | (√6 − √2)/4 ≈ 0.258819 |
| tan 75° | 2 + √3 ≈ 3.732051 |
75° on a protractor
How to draw a 75° 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 75° 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 75°.
Drawing it a 75° angle without a protractor (compass and ruler)
- Draw a 90° angle: construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- Inside it, starting from the second arm, mark a 15° angle: construct a 30° angle, then bisect it.
- What is left between the first arm and the new line is 90° − 15° = 75°.
Where you see 75° angles
- The 4-to-1 ladder rule (1 foot out for every 4 feet up) sets a ladder at about 76°, near the 75.5° that ladder safety guidelines recommend.
- 75° of latitude on Earth spans roughly 5,179 miles north to south.
- The Earth turns 75° on its axis in about 5 hours.
- Narrow acute angles like 75° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
75° angle FAQ
What type of angle is 75°?
A 75° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 75°?
The complement of 75° is 15° (together they make 90°), and the supplement is 105° (together they make 180°).
How many radians is 75 degrees?
75° = 5π/12 radians ≈ 1.309 rad. To convert degrees to radians, multiply by π/180: 75 × π/180 = 5π/12.
How do I measure a 75° angle on my screen?
Open the online protractor with 75° preset, or type 75 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
