A 42° angle is an acute angle: it is smaller than a right angle (90°). It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 48°.
42° is 7/60 of a full circle, or 7π/30 radians. The minute hand of a clock sweeps 42° in 7 minutes. If you face north and turn 42° clockwise, you end up facing between NNE and NE (closest to northeast (NE)).
42° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 48° |
| Supplement (adds to 180°) | 138° |
| Explement (adds to 360°) | 318° |
| Radians | 7π/30 ≈ 0.733038 |
| Gradians | 46.6667 grad |
| Fraction of a turn | 7/60 (11.67%) |
| Degrees, minutes, seconds | 42° 0′ 0″ |
| Slope (grade) | 90.04% |
| Roof pitch | 10.8/12 |
| Compass bearing | between NNE and NE (closest to northeast (NE)) |
Trigonometric values of 42°
| Function | Value |
|---|---|
| sin 42° | 0.669131 |
| cos 42° | 0.743145 |
| tan 42° | 0.900404 |
42° on a protractor
How to draw a 42° 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 42° 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 42°.
Drawing it a 42° 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 9 inches (about 9″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 42°, because tan 42° ≈ 0.9004.
Where you see 42° angles
- A rainbow is a circle of light about 42° from the point directly opposite the sun.
- A 11/12 roof pitch is 42.51°, very close to 42°.
- A board sloped at 42° rises about 108 inches over a 10-foot (120-inch) run.
- 42° of latitude on Earth spans roughly 2,900 miles north to south.
- The Earth turns 42° on its axis in about 2 h 48 min.
Related angles
42° angle FAQ
What type of angle is 42°?
A 42° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 42°?
The complement of 42° is 48° (together they make 90°), and the supplement is 138° (together they make 180°).
How many radians is 42 degrees?
42° = 7π/30 radians ≈ 0.733 rad. To convert degrees to radians, multiply by π/180: 42 × π/180 = 7π/30.
What is 42° as a slope or roof pitch?
42° is a 90% slope, which is a roof pitch of 10.8/12 (a rise of about 10 3/4 inches for every 12 inches of run).
