A 69° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 21° more and you get a square corner.
69° is 23/120 of a full circle, or 23π/60 radians. If you face north and turn 69° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
69° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 21° |
| Supplement (adds to 180°) | 111° |
| Explement (adds to 360°) | 291° |
| Radians | 23π/60 ≈ 1.204277 |
| Gradians | 76.6667 grad |
| Fraction of a turn | 23/120 (19.17%) |
| Degrees, minutes, seconds | 69° 0′ 0″ |
| Slope (grade) | 260.51% |
| Roof pitch | 31.26/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 69°
| Function | Value |
|---|---|
| sin 69° | 0.93358 |
| cos 69° | 0.358368 |
| tan 69° | 2.605089 |
69° on a protractor
How to draw a 69° 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 69° 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 69°.
Drawing it a 69° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 3.84 inches (about 3 13/16″) 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 69°, because tan 69° ≈ 2.6051.
Where you see 69° angles
- 69° of latitude on Earth spans roughly 4,764 miles north to south.
- The Earth turns 69° on its axis in about 4 h 36 min.
- Narrow acute angles like 69° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
69° angle FAQ
What type of angle is 69°?
A 69° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 69°?
The complement of 69° is 21° (together they make 90°), and the supplement is 111° (together they make 180°).
How many radians is 69 degrees?
69° = 23π/60 radians ≈ 1.2043 rad. To convert degrees to radians, multiply by π/180: 69 × π/180 = 23π/60.
What is 69° as a slope or roof pitch?
69° is a 260.5% slope, which is a roof pitch of 31.26/12 (a rise of about 31 1/4 inches for every 12 inches of run).
