A 50° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 40° more and you get a square corner.
50° is 5/36 of a full circle, or 5π/18 radians. If you face north and turn 50° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
50° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 40° |
| Supplement (adds to 180°) | 130° |
| Explement (adds to 360°) | 310° |
| Radians | 5π/18 ≈ 0.872665 |
| Gradians | 55.5556 grad |
| Fraction of a turn | 5/36 (13.89%) |
| Degrees, minutes, seconds | 50° 0′ 0″ |
| Slope (grade) | 119.18% |
| Roof pitch | 14.3/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 50°
| Function | Value |
|---|---|
| sin 50° | 0.766044 |
| cos 50° | 0.642788 |
| tan 50° | 1.191754 |
50° on a protractor
How to draw a 50° 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 50° 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 50°.
Drawing it a 50° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 8.39 inches (about 8 3/8″) 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 50°, because tan 50° ≈ 1.1918.
Where you see 50° angles
- A board sloped at 50° rises about 143 inches over a 10-foot (120-inch) run.
- 50° of latitude on Earth spans roughly 3,453 miles north to south.
- The Earth turns 50° on its axis in about 3 h 20 min.
- Narrow acute angles like 50° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
50° angle FAQ
What type of angle is 50°?
A 50° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 50°?
The complement of 50° is 40° (together they make 90°), and the supplement is 130° (together they make 180°).
How many radians is 50 degrees?
50° = 5π/18 radians ≈ 0.8727 rad. To convert degrees to radians, multiply by π/180: 50 × π/180 = 5π/18.
What is 50° as a slope or roof pitch?
50° is a 119.2% slope, which is a roof pitch of 14.3/12 (a rise of about 14 1/4 inches for every 12 inches of run).
