A 339° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 21° angle: together they make a full 360° circle.
339° is 113/120 of a full circle, or 113π/60 radians. If you face north and turn 339° clockwise, you end up facing between NNW and N (closest to north-northwest (NNW)).
339° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 21° |
| Radians | 113π/60 ≈ 5.916666 |
| Gradians | 376.6667 grad |
| Fraction of a turn | 113/120 (94.17%) |
| Degrees, minutes, seconds | 339° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north-northwest (NNW)) |
Trigonometric values of 339°
| Function | Value |
|---|---|
| sin 339° | −0.358368 |
| cos 339° | 0.93358 |
| tan 339° | −0.383864 |
339° on a protractor
How to draw a 339° angle with a protractor
- Subtract from 360°: 360° − 339° = 21°. 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 21°.
- Join the vertex to the dot. The inside angle is 21°; the outside angle, going the long way around, is 339°. Draw the angle arc on the outside and label it 339°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 339° directly.
Drawing it a 339° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 3.84 inches (about 3 13/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 21°, because tan 21° ≈ 0.3839.
- That gives you 21°. The outside (reflex) angle is 339°.
Where you see 339° angles
- The Earth turns 339° on its axis in about 22 h 36 min.
- A 339° 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
339° angle FAQ
What type of angle is 339°?
A 339° angle is a reflex angle, because it is between 180° and 360°.
Does a 339° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 339° is already larger than both. What it does have is an explement (conjugate) of 21°, the angle that completes a full 360° circle.
How many radians is 339 degrees?
339° = 113π/60 radians ≈ 5.9167 rad. To convert degrees to radians, multiply by π/180: 339 × π/180 = 113π/60.
How do I measure a 339° angle on my screen?
Open the online protractor with 339° preset, or type 339 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
