An 8° angle is classed as acute because it measures less than 90°. It is a very narrow angle, just 8.9% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
8° is one forty-fifth (1/45) of a full circle, or 2π/45 radians. If you face north and turn 8° clockwise, you end up facing between N and NNE (closest to north (N)).
8° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 82° |
| Supplement (adds to 180°) | 172° |
| Explement (adds to 360°) | 352° |
| Radians | 2π/45 ≈ 0.139626 |
| Gradians | 8.8889 grad |
| Fraction of a turn | one forty-fifth (1/45) (2.22%) |
| Degrees, minutes, seconds | 8° 0′ 0″ |
| Slope (grade) | 14.05% |
| Roof pitch | 1.69/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 8°
| Function | Value |
|---|---|
| sin 8° | 0.139173 |
| cos 8° | 0.990268 |
| tan 8° | 0.140541 |
8° on a protractor
How to draw an 8° 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 8° 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 8°.
Drawing it an 8° 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 1.41 inches (about 1 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 8°, because tan 8° ≈ 0.1405.
Where you see 8° angles
- Divide a circle into 45 equal slices and each slice is 8°, e.g. 45 spokes on a wheel or 45 equal pie-chart wedges.
- A board sloped at 8° rises about 16.9 inches over a 10-foot (120-inch) run.
- 8° of latitude on Earth spans roughly 552 miles north to south.
- The Earth turns 8° on its axis in about 32 minutes.
Related angles
8° angle FAQ
What type of angle is 8°?
An 8° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 8°?
The complement of 8° is 82° (together they make 90°), and the supplement is 172° (together they make 180°).
How many radians is 8 degrees?
8° = 2π/45 radians ≈ 0.1396 rad. To convert degrees to radians, multiply by π/180: 8 × π/180 = 2π/45.
What is 8° as a slope or roof pitch?
8° is a 14.1% slope, which is a roof pitch of 1.69/12 (a rise of about 1 5/8 inches for every 12 inches of run).
