Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.5   b = 4.2   c = 4.66

Area: T = 7.06601840656
Perimeter: p = 12.36
Semiperimeter: s = 6.18

Angle ∠ A = α = 46.17549540127° = 46°10'30″ = 0.80659049795 rad
Angle ∠ B = β = 59.96883552323° = 59°58'6″ = 1.04766452458 rad
Angle ∠ C = γ = 73.85766907551° = 73°51'24″ = 1.28990424283 rad

Height: ha = 4.03443908946
Height: hb = 3.36219924122
Height: hc = 3.03301219166

Median: ma = 4.07661869437
Median: mb = 3.54658144339
Median: mc = 3.08548176607

Inradius: r = 1.14224246061
Circumradius: R = 2.42656449748

Vertex coordinates: A[4.66; 0] B[0; 0] C[1.75216738197; 3.03301219166]
Centroid: CG[2.13772246066; 1.01100406389]
Coordinates of the circumscribed circle: U[2.33; 0.67444283089]
Coordinates of the inscribed circle: I[1.98; 1.14224246061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.8255045987° = 133°49'30″ = 0.80659049795 rad
∠ B' = β' = 120.0321644768° = 120°1'54″ = 1.04766452458 rad
∠ C' = γ' = 106.1433309245° = 106°8'36″ = 1.28990424283 rad

Calculate another triangle




How did we calculate this triangle?

a = 3.5 ; ; b = 4.2 ; ; c = 4.66 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 3.5+4.2+4.66 = 12.36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.36 }{ 2 } = 6.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.18 * (6.18-3.5)(6.18-4.2)(6.18-4.66) } ; ; T = sqrt{ 49.85 } = 7.06 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.06 }{ 3.5 } = 4.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.06 }{ 4.2 } = 3.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.06 }{ 4.66 } = 3.03 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 3.5**2-4.2**2-4.66**2 }{ 2 * 4.2 * 4.66 } ) = 46° 10'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.2**2-3.5**2-4.66**2 }{ 2 * 3.5 * 4.66 } ) = 59° 58'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.66**2-3.5**2-4.2**2 }{ 2 * 4.2 * 3.5 } ) = 73° 51'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.06 }{ 6.18 } = 1.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.5 }{ 2 * sin 46° 10'30" } = 2.43 ; ;

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.