A 35° angle is classed as acute because it measures less than 90°. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 55°.
35° is 7/72 of a full circle, or 7π/36 radians. If you face north and turn 35° clockwise, you end up facing between NNE and NE (closest to northeast (NE)).
35° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 55° |
| Supplement (adds to 180°) | 145° |
| Explement (adds to 360°) | 325° |
| Radians | 7π/36 ≈ 0.610865 |
| Gradians | 38.8889 grad |
| Fraction of a turn | 7/72 (9.72%) |
| Degrees, minutes, seconds | 35° 0′ 0″ |
| Slope (grade) | 70.02% |
| Roof pitch | 8.4/12 |
| Compass bearing | between NNE and NE (closest to northeast (NE)) |
Trigonometric values of 35°
| Function | Value |
|---|---|
| sin 35° | 0.573576 |
| cos 35° | 0.819152 |
| tan 35° | 0.700208 |
35° on a protractor
How to draw a 35° 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 35° 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 35°.
Drawing it a 35° 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 7 inches (about 7″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 35°, because tan 35° ≈ 0.7002.
Where you see 35° angles
- Most avalanches release on slopes between about 30° and 45°, which is why backcountry skiers watch for 35° slopes.
- A board sloped at 35° rises about 84 inches over a 10-foot (120-inch) run.
- 35° of latitude on Earth spans roughly 2,417 miles north to south.
- The Earth turns 35° on its axis in about 2 h 20 min.
Related angles
35° angle FAQ
What type of angle is 35°?
A 35° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 35°?
The complement of 35° is 55° (together they make 90°), and the supplement is 145° (together they make 180°).
How many radians is 35 degrees?
35° = 7π/36 radians ≈ 0.6109 rad. To convert degrees to radians, multiply by π/180: 35 × π/180 = 7π/36.
What is 35° as a slope or roof pitch?
35° is a 70% slope, which is a roof pitch of 8.4/12 (a rise of about 8 3/8 inches for every 12 inches of run).
