This triangle calculator solves triangle properties given any three known values (sides or angles). It computes the area, perimeter, and remaining unknown sides and angles using trigonometry and geometry rules.
Formula Used
Area = √[s(s − a)(s − b)(s − c)] (Heron's Formula)
Area = 0.5 × a × b × sin(C)
a / b / c
— the lengths of the three sides of the triangle
s
— semi-perimeter = (a + b + c) ÷ 2
C
— the angle opposite side c, in degrees
Example Calculation
For a triangle with side lengths a = 3, b = 4, and c = 5: s = (3+4+5)/2 = 6. Area = √[6 × (6-3) × (6-4) × (6-5)] = √[6 × 3 × 2 × 1] = √36 = 6. The perimeter is 3 + 4 + 5 = 12.
Frequently Asked Questions
Heron's formula is a geometric formula that calculates the area of a triangle using only its three side lengths, without needing to know the height.
The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C).
No. The sum of all angles in a triangle is exactly 180 degrees. Since an obtuse angle is greater than 90 degrees, two obtuse angles would exceed 180 degrees.
An equilateral triangle is a triangle where all three sides are equal in length and all three internal angles are exactly 60 degrees.
A triangle is invalid if the sum of any two side lengths is not greater than the length of the remaining side (known as the Triangle Inequality Theorem).