At 289°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 71° angle: together they make a full 360° circle.
289° is 289/360 of a full circle, or 289π/180 radians. If you face north and turn 289° clockwise, you end up facing between W and WNW (closest to west-northwest (WNW)).
289° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 71° |
| Radians | 289π/180 ≈ 5.044002 |
| Gradians | 321.1111 grad |
| Fraction of a turn | 289/360 (80.28%) |
| Degrees, minutes, seconds | 289° 0′ 0″ |
| Compass bearing | between W and WNW (closest to west-northwest (WNW)) |
Trigonometric values of 289°
| Function | Value |
|---|---|
| sin 289° | −0.945519 |
| cos 289° | 0.325568 |
| tan 289° | −2.904211 |
289° on a protractor
How to draw a 289° angle with a protractor
- Subtract from 360°: 360° − 289° = 71°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 71°.
- Join the vertex to the dot. The inside angle is 71°; the outside angle, going the long way around, is 289°. Draw the angle arc on the outside and label it 289°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 289° directly.
Drawing it a 289° 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.
- That gives you 71°. The outside (reflex) angle is 289°.
Where you see 289° angles
- The Earth turns 289° on its axis in about 19 h 16 min.
- A 289° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
289° angle FAQ
What type of angle is 289°?
A 289° angle is a reflex angle, because it is between 180° and 360°.
Does a 289° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 289° is already larger than both. What it does have is an explement (conjugate) of 71°, the angle that completes a full 360° circle.
How many radians is 289 degrees?
289° = 289π/180 radians ≈ 5.044 rad. To convert degrees to radians, multiply by π/180: 289 × π/180 = 289π/180.
How do I measure a 289° angle on my screen?
Open the online protractor with 289° preset, or type 289 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
