A 48° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 42° more and you get a square corner.
48° is 2/15 of a full circle, or 4π/15 radians. The minute hand of a clock sweeps 48° in 8 minutes. If you face north and turn 48° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
48° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 42° |
| Supplement (adds to 180°) | 132° |
| Explement (adds to 360°) | 312° |
| Radians | 4π/15 ≈ 0.837758 |
| Gradians | 53.3333 grad |
| Fraction of a turn | 2/15 (13.33%) |
| Degrees, minutes, seconds | 48° 0′ 0″ |
| Slope (grade) | 111.06% |
| Roof pitch | 13.33/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 48°
| Function | Value |
|---|---|
| sin 48° | 0.743145 |
| cos 48° | 0.669131 |
| tan 48° | 1.110613 |
48° on a protractor
How to draw a 48° 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 48° 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 48°.
Drawing it a 48° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 9 inches (about 9″) 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 48°, because tan 48° ≈ 1.1106.
Where you see 48° angles
- A board sloped at 48° rises about 133.3 inches over a 10-foot (120-inch) run.
- 48° of latitude on Earth spans roughly 3,314 miles north to south.
- The Earth turns 48° on its axis in about 3 h 12 min.
- Narrow acute angles like 48° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
48° angle FAQ
What type of angle is 48°?
A 48° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 48°?
The complement of 48° is 42° (together they make 90°), and the supplement is 132° (together they make 180°).
How many radians is 48 degrees?
48° = 4π/15 radians ≈ 0.8378 rad. To convert degrees to radians, multiply by π/180: 48 × π/180 = 4π/15.
What is 48° as a slope or roof pitch?
48° is a 111.1% slope, which is a roof pitch of 13.33/12 (a rise of about 13 3/8 inches for every 12 inches of run).
