A 71° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 19° more and you get a square corner.
71° is 71/360 of a full circle, or 71π/180 radians. If you face north and turn 71° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
71° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 19° |
| Supplement (adds to 180°) | 109° |
| Explement (adds to 360°) | 289° |
| Radians | 71π/180 ≈ 1.239184 |
| Gradians | 78.8889 grad |
| Fraction of a turn | 71/360 (19.72%) |
| Degrees, minutes, seconds | 71° 0′ 0″ |
| Slope (grade) | 290.42% |
| Roof pitch | 34.85/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 71°
| Function | Value |
|---|---|
| sin 71° | 0.945519 |
| cos 71° | 0.325568 |
| tan 71° | 2.904211 |
71° on a protractor
How to draw a 71° 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 71° 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 71°.
Drawing it a 71° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 3.44 inches (about 3 7/16″) 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 71°, because tan 71° ≈ 2.9042.
Where you see 71° angles
- 71° of latitude on Earth spans roughly 4,903 miles north to south.
- The Earth turns 71° on its axis in about 4 h 44 min.
- Narrow acute angles like 71° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
71° angle FAQ
What type of angle is 71°?
A 71° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 71°?
The complement of 71° is 19° (together they make 90°), and the supplement is 109° (together they make 180°).
How many radians is 71 degrees?
71° = 71π/180 radians ≈ 1.2392 rad. To convert degrees to radians, multiply by π/180: 71 × π/180 = 71π/180.
How do I measure a 71° angle on my screen?
Open the online protractor with 71° preset, or type 71 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
