Advanced Triangle Calculator
Triangle Specifications
Area:
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Perimeter:
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Semi-perimeter:
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Angle A (opposite side A):
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Angle B (opposite side B):
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Angle C (opposite side C):
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Triangle Type:
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How to Use the Triangle Calculator
This triangle calculator helps you find all the geometric properties of a triangle based on the lengths of its three sides. Simply enter the values for Side A, Side B, and Side C to instantly calculate the area, perimeter, and all internal angles.
Heron's Formula for Triangle Area
When the heights of a triangle are unknown, we use Heron's Formula to find the area using only the side lengths. First, we calculate the semi-perimeter (s):
s = (a + b + c) / 2
Then, the area (A) is calculated as:
Area = √[s × (s – a) × (s – b) × (s – c)]
Understanding Triangle Classifications
Our calculator also identifies the specific type of triangle based on the inputs provided:
- Equilateral: All three sides are equal in length.
- Isosceles: At least two sides are equal in length.
- Scalene: All three sides have different lengths.
- Right-Angled: One angle is exactly 90 degrees (follows the Pythagorean theorem: a² + b² = c²).
The Triangle Inequality Theorem
For three lengths to form a valid triangle, the sum of the lengths of any two sides must be strictly greater than the length of the third side. If this condition is not met, the sides cannot connect to form a closed polygon. For example, lengths of 1, 2, and 10 cannot form a triangle because 1 + 2 is not greater than 10.
Internal Angles and the Law of Cosines
To find the internal angles when three sides are known, the calculator utilizes the Law of Cosines. The formula for Angle A is:
cos(A) = (b² + c² – a²) / (2bc)
By applying the inverse cosine (arccos) to this result, we determine the angle in degrees. The sum of all internal angles in a triangle will always equal 180 degrees.