This calculator can give out all of the edges, angles, the total area, as well as a diagram of how the triangle will look like based on three input parameters.
Please provide 3 positive values to any of the following 6 fields and click "Calculate" button to use.
The following are some basic facts and theorems of a triangle.
Angles and Sides of a Triangle
- The interior angles of a triangle are always added up to 180 degrees. The exterior angle of a triangle is equal to the sum of the two interior angles that are not adjacent to it.
- The sum of the lengths of any two sides of a triangle is always larger than the length of the third.
- Pythagorean theorem—in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. Conversely, if the lengths of the sides of a triangle satisfy the above condition, the angle opposite to the longest side is a right angle.
- Sine rule—the ratio of the length of a side to the sine of its opposite angle is constant
x/sin(b) = y/sin(a) = z/sin(c)
- The angle of a triangle can be calculated from its sides
a = arccos((x2 + y2 + z2)/2xz)
b = arccos((x2 + y2 + z2)/2yz)
c = arccos((x2 + y2 + z2)/2xy)
Area of a Triangle:
- If the length of the base and the height are known.
Area = ½bh
Where b is the length of the base and h is the height on the base.
- If length of two sides and the angle between them are known.
Area = ½xy sin(c) = ½xz sin(a) = ½yz sin(b)
- Heron's formula—if the length of the three sides are known.
Area = (s(s-x)(s-y)(s-z))½
where s = ½(x + y + z)