An 87° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 3° more and you get a square corner.
87° is 29/120 of a full circle, or 29π/60 radians. If you face north and turn 87° clockwise, you end up facing between ENE and E (closest to east (E)).
87° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 3° |
| Supplement (adds to 180°) | 93° |
| Explement (adds to 360°) | 273° |
| Radians | 29π/60 ≈ 1.518436 |
| Gradians | 96.6667 grad |
| Fraction of a turn | 29/120 (24.17%) |
| Degrees, minutes, seconds | 87° 0′ 0″ |
| Slope (grade) | 1908.11% |
| Roof pitch | 228.97/12 |
| Compass bearing | between ENE and E (closest to east (E)) |
Trigonometric values of 87°
| Function | Value |
|---|---|
| sin 87° | 0.99863 |
| cos 87° | 0.052336 |
| tan 87° | 19.081137 |
87° on a protractor
How to draw an 87° 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 87° 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 87°.
Drawing it an 87° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 0.52 inches (about 1/2″) 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 87°, because tan 87° ≈ 19.0811.
Where you see 87° angles
- 87° of latitude on Earth spans roughly 6,007 miles north to south.
- The Earth turns 87° on its axis in about 5 h 48 min.
- Narrow acute angles like 87° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
87° angle FAQ
What type of angle is 87°?
An 87° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 87°?
The complement of 87° is 3° (together they make 90°), and the supplement is 93° (together they make 180°).
How many radians is 87 degrees?
87° = 29π/60 radians ≈ 1.5184 rad. To convert degrees to radians, multiply by π/180: 87 × π/180 = 29π/60.
How do I measure an 87° angle on my screen?
Open the online protractor with 87° preset, or type 87 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
