At 46°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 44° more and you get a square corner.
46° is 23/180 of a full circle, or 23π/90 radians. If you face north and turn 46° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
46° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 44° |
| Supplement (adds to 180°) | 134° |
| Explement (adds to 360°) | 314° |
| Radians | 23π/90 ≈ 0.802851 |
| Gradians | 51.1111 grad |
| Fraction of a turn | 23/180 (12.78%) |
| Degrees, minutes, seconds | 46° 0′ 0″ |
| Slope (grade) | 103.55% |
| Roof pitch | 12.43/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 46°
| Function | Value |
|---|---|
| sin 46° | 0.71934 |
| cos 46° | 0.694658 |
| tan 46° | 1.03553 |
46° on a protractor
How to draw a 46° 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 46° 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 46°.
Drawing it a 46° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 9.66 inches (about 9 11/16″) 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 46°, because tan 46° ≈ 1.0355.
Where you see 46° angles
- A board sloped at 46° rises about 124.3 inches over a 10-foot (120-inch) run.
- 46° of latitude on Earth spans roughly 3,176 miles north to south.
- The Earth turns 46° on its axis in about 3 h 4 min.
- Narrow acute angles like 46° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
46° angle FAQ
What type of angle is 46°?
A 46° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 46°?
The complement of 46° is 44° (together they make 90°), and the supplement is 134° (together they make 180°).
How many radians is 46 degrees?
46° = 23π/90 radians ≈ 0.8029 rad. To convert degrees to radians, multiply by π/180: 46 × π/180 = 23π/90.
What is 46° as a slope or roof pitch?
46° is a 103.6% slope, which is a roof pitch of 12.43/12 (a rise of about 12 3/8 inches for every 12 inches of run).
