Triangle Calculator

Triangle Calculator

A triangle is a polygon with three vertices (corners). A vertex is the point where two edges meet. The three vertices of a triangle are connected by three edges (sides). Triangles are typically labeled by their vertices, so a triangle with vertices A, B, and C is commonly denoted as ΔABC.

Types of Triangles by Side Length:

• Equilateral Triangle – All three sides are of equal length.
• Isosceles Triangle – Two sides are of equal length.
• Scalene Triangle – No sides are of equal length.

Types of Triangles by Angle:

• Right Triangle – One angle equals 90°. The longest side is called the hypotenuse.
• Oblique Triangle – No angle is 90°. These can be:
  • Acute Triangle – All angles less than 90°.
  • Obtuse Triangle – One angle greater than 90°.

Key Properties of Triangles:

• Interior angles always add up to 180°.
• The exterior angle equals the sum of the two non-adjacent interior angles.
• The sum of any two sides is always greater than the third side.

Pythagorean Theorem (Right Triangles Only):

a² + b² = c²

Example: Given a = 3, c = 5, find b:

3² + b² = 5² → 9 + b² = 25 → b² = 16 → b = 4

Law of Sines:

a / sin(A) = b / sin(B) = c / sin(C)

Example: Given b = 2, B = 90°, C = 45°:

2 / sin(90°) = c / sin(45°) → c = √2

Law of Cosines (When All Sides Are Known):

A = arccos((b² + c² - a²) / 2bc)

B = arccos((a² + c² - b²) / 2ac)

C = arccos((a² + b² - c²) / 2ab)

Example: a = 8, b = 6, c = 10, B = 36.87°

Area of a Triangle:

Using Base and Height:

Area = 1/2 × base × height

Example: Base = 5, Height = 6 → Area = 15

Using Two Sides and Included Angle:

Area = 1/2 × a × b × sin(C)

Example: a = 9, b = 7, C = 30° → Area = 15.75

Using Heron’s Formula:

s = (a + b + c) / 2

Area = √(s(s - a)(s - b)(s - c))

Example: a = 3, b = 4, c = 5 → Area = 6

Additional Triangle Elements:

Median:

The median connects a vertex to the midpoint of the opposite side. All medians intersect at the centroid (center of gravity).

Inradius (r):

Inradius = Area / s

s = (a + b + c) / 2

Circumradius (R):

Circumradius = a / (2sin(A))

The circumcenter is the point from which the circumradius is measured and may lie inside or outside the triangle.

Related Calculator:
Slope Calculator, Hexadecimal Calculator, Log Calculator 

External Resources:
Triangle Calculator on  Calculator.net