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Complete Results
Side a
3.000000
Side b
4.000000
Side c
5.000000
Angle A
36.8699 deg
Angle B
53.1301 deg
Angle C
90.0000 deg
Area
6.000000
Perimeter
12.000000
Semi-perimeter
6.000000
Type
Scalene Right
Heights (Altitudes)
Medians
Inradius (inscribed circle)
1.000000
Circumradius (circumscribed circle)
2.500000
Triangle Centers
Coordinates relative to vertex C at origin, with B along positive x-axis.
Centroid (G)
Intersection of medians
(1.0000, 1.3333)
Incenter (I)
Intersection of angle bisectors
(1.0000, 1.0000)
Circumcenter (O)
Intersection of perp. bisectors
(1.5000, 2.0000)
Orthocenter (H)
Intersection of altitudes
(0.0000, 0.0000)
Euler Line: In any non-equilateral triangle, the centroid (G), circumcenter (O), and orthocenter (H) are collinear, with G dividing OH in ratio 1:2.
Step-by-Step Solution
Triangle Formulas
Area Formulas:
Area = (1/2) x base x height
Area = (1/2) x a x b x sin(C)
Area = sqrt(s(s-a)(s-b)(s-c)) (Heron's formula)
Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(C)
Used for: SSS (find angles), SAS (find third side)
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Used for: ASA, AAS, SSA (with ambiguous case check)
Radii:
Inradius r = Area / s
Circumradius R = abc / (4 x Area)
Common Special Triangles
3-4-5 Right Triangle
Sides: 3, 4, 5
Angles: 36.87 deg, 53.13 deg, 90 deg
Multiples work too: 6-8-10, 9-12-15
45-45-90 Triangle
Sides ratio: 1 : 1 : sqrt(2)
Isosceles right triangle
Example: 1, 1, 1.414...
30-60-90 Triangle
Sides ratio: 1 : sqrt(3) : 2
Half of equilateral triangle
Example: 1, 1.732, 2
Equilateral Triangle
All sides equal, all angles 60 deg
Area = (sqrt(3)/4) x side^2
Height = (sqrt(3)/2) x side
Triangle Properties
Area
6.0000
square units
Perimeter
12.0000
units
?How to Calculate Triangle Properties
Triangle area = (base x height) / 2, or using Heron's formula: sqrt(s(s-a)(s-b)(s-c)) where s is semi-perimeter. The sum of interior angles always equals 180 degrees. Use Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c squared = a squared + b squared - 2ab cosC) to solve triangles.
What is a Triangle?
A triangle is a polygon with three sides and three angles. The sum of interior angles is always 180 degrees. Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Triangle calculators use trigonometric laws to find unknown measurements from given values.
Key Facts About Triangles
- Sum of interior angles always equals 180 degrees
- Area = (base x height) / 2, or use Heron's formula with three sides
- Perimeter = sum of all three sides (a + b + c)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- Law of Cosines: c squared = a squared + b squared - 2ab*cos(C)
- Triangle inequality: any side must be less than the sum of the other two
- Equilateral: all sides and angles equal (60 degrees each)
- Isosceles: two equal sides and two equal base angles
Practice Triangle Problems
Test your understanding of triangle calculations
Practice with 6 problems to test your understanding.
Related Geometry Tools
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Quick Answer
Triangle area = (base x height) / 2, or using Heron's formula: sqrt(s(s-a)(s-b)(s-c)) where s is semi-perimeter. The sum of interior angles always equals 180 degrees. Use Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c squared = a squared + b squared - 2ab cosC) to solve triangles.
Frequently Asked Questions
How do I calculate the area of a triangle?
For base and height: Area = (1/2) x base x height. For three sides (Heron's formula): s = (a+b+c)/2, Area = sqrt(s(s-a)(s-b)(s-c)). For two sides and included angle: Area = (1/2) x a x b x sin(C).
What is the ambiguous case (SSA)?
When you know two sides and an angle opposite to one of them (SSA), there may be zero, one, or two possible triangles. This happens because the sine function gives the same value for an angle and its supplement. Always check for the second solution!
What is the Law of Cosines?
c^2 = a^2 + b^2 - 2ab*cos(C). This generalizes Pythagorean theorem to any triangle. Use it to find a side when you know two sides and the included angle, or to find angles when you know all three sides.
What is the Law of Sines?
a/sin(A) = b/sin(B) = c/sin(C). Each side divided by the sine of its opposite angle gives the same ratio. Use it when you know a side-angle pair plus one other measurement.
What are the triangle centers?
Centroid: intersection of medians (center of mass). Incenter: intersection of angle bisectors (center of inscribed circle). Circumcenter: intersection of perpendicular bisectors (center of circumscribed circle). Orthocenter: intersection of altitudes.
What are the different triangle types?
By sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal). By angles: Acute (all < 90 deg), Right (one = 90 deg), Obtuse (one > 90 deg). A triangle can be described by both, e.g., "Isosceles Right".
Last updated: 2026-01-15
How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
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