A 297° 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 63° angle: together they make a full 360° circle.
297° is 33/40 of a full circle, or 33π/20 radians. If you face north and turn 297° clockwise, you end up facing between WNW and NW (closest to west-northwest (WNW)).
297° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 63° |
| Radians | 33π/20 ≈ 5.183628 |
| Gradians | 330 grad |
| Fraction of a turn | 33/40 (82.5%) |
| Degrees, minutes, seconds | 297° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to west-northwest (WNW)) |
Trigonometric values of 297°
| Function | Value |
|---|---|
| sin 297° | −0.891007 |
| cos 297° | 0.45399 |
| tan 297° | −1.962611 |
297° on a protractor
How to draw a 297° angle with a protractor
- Subtract from 360°: 360° − 297° = 63°. 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 63°.
- Join the vertex to the dot. The inside angle is 63°; the outside angle, going the long way around, is 297°. Draw the angle arc on the outside and label it 297°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 297° directly.
Drawing it a 297° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 5.1 inches (about 5 1/8″) 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 63°, because tan 63° ≈ 1.9626.
- That gives you 63°. The outside (reflex) angle is 297°.
Where you see 297° angles
- The Earth turns 297° on its axis in about 19 h 48 min.
- A 297° 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
297° angle FAQ
What type of angle is 297°?
A 297° angle is a reflex angle, because it is between 180° and 360°.
Does a 297° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 297° is already larger than both. What it does have is an explement (conjugate) of 63°, the angle that completes a full 360° circle.
How many radians is 297 degrees?
297° = 33π/20 radians ≈ 5.1836 rad. To convert degrees to radians, multiply by π/180: 297 × π/180 = 33π/20.
How do I measure a 297° angle on my screen?
Open the online protractor with 297° preset, or type 297 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
