At 49°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 41° more and you get a square corner.
49° is 49/360 of a full circle, or 49π/180 radians. If you face north and turn 49° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
49° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 41° |
| Supplement (adds to 180°) | 131° |
| Explement (adds to 360°) | 311° |
| Radians | 49π/180 ≈ 0.855211 |
| Gradians | 54.4444 grad |
| Fraction of a turn | 49/360 (13.61%) |
| Degrees, minutes, seconds | 49° 0′ 0″ |
| Slope (grade) | 115.04% |
| Roof pitch | 13.8/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 49°
| Function | Value |
|---|---|
| sin 49° | 0.75471 |
| cos 49° | 0.656059 |
| tan 49° | 1.150368 |
49° on a protractor
How to draw a 49° 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 49° 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 49°.
Drawing it a 49° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 8.69 inches (about 8 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 49°, because tan 49° ≈ 1.1504.
Where you see 49° angles
- A 14/12 roof pitch is 49.4°, very close to 49°.
- A board sloped at 49° rises about 138 inches over a 10-foot (120-inch) run.
- 49° of latitude on Earth spans roughly 3,383 miles north to south.
- The Earth turns 49° on its axis in about 3 h 16 min.
Related angles
49° angle FAQ
What type of angle is 49°?
A 49° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 49°?
The complement of 49° is 41° (together they make 90°), and the supplement is 131° (together they make 180°).
How many radians is 49 degrees?
49° = 49π/180 radians ≈ 0.8552 rad. To convert degrees to radians, multiply by π/180: 49 × π/180 = 49π/180.
What is 49° as a slope or roof pitch?
49° is a 115% slope, which is a roof pitch of 13.8/12 (a rise of about 13 3/4 inches for every 12 inches of run).
