An 89° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 1° more and you get a square corner.
89° is 89/360 of a full circle, or 89π/180 radians. If you face north and turn 89° clockwise, you end up facing between ENE and E (closest to east (E)).
89° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 1° |
| Supplement (adds to 180°) | 91° |
| Explement (adds to 360°) | 271° |
| Radians | 89π/180 ≈ 1.553343 |
| Gradians | 98.8889 grad |
| Fraction of a turn | 89/360 (24.72%) |
| Degrees, minutes, seconds | 89° 0′ 0″ |
| Slope (grade) | 5729% |
| Roof pitch | 687.48/12 |
| Compass bearing | between ENE and E (closest to east (E)) |
Trigonometric values of 89°
| Function | Value |
|---|---|
| sin 89° | 0.999848 |
| cos 89° | 0.017452 |
| tan 89° | 57.289962 |
89° on a protractor
How to draw an 89° 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 89° 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 89°.
Drawing it an 89° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 0.17 inches (about 3/16″) 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 89°, because tan 89° ≈ 57.29.
Where you see 89° angles
- 89° of latitude on Earth spans roughly 6,145 miles north to south.
- The Earth turns 89° on its axis in about 5 h 56 min.
- Narrow acute angles like 89° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
89° angle FAQ
What type of angle is 89°?
An 89° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 89°?
The complement of 89° is 1° (together they make 90°), and the supplement is 91° (together they make 180°).
How many radians is 89 degrees?
89° = 89π/180 radians ≈ 1.5533 rad. To convert degrees to radians, multiply by π/180: 89 × π/180 = 89π/180.
How do I measure an 89° angle on my screen?
Open the online protractor with 89° preset, or type 89 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
