Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 264.39   b = 254.22   c = 132.2

Area: T = 16524.71099057
Perimeter: p = 650.81
Semiperimeter: s = 325.405

Angle ∠ A = α = 79.54403309817° = 79°32'25″ = 1.38882406638 rad
Angle ∠ B = β = 71.00766275549° = 71°24″ = 1.23992994416 rad
Angle ∠ C = γ = 29.45330414635° = 29°27'11″ = 0.51440525483 rad

Height: ha = 125.0032533422
Height: hb = 130.0033224811
Height: hc = 249.9965611281

Median: ma = 153.547740693
Median: mb = 165.9299213673
Median: mc = 250.7990211631

Inradius: r = 50.78219790897
Circumradius: R = 134.4298811481

Vertex coordinates: A[132.2; 0] B[0; 0] C[86.04880472769; 249.9965611281]
Centroid: CG[72.74993490923; 83.33218704271]
Coordinates of the circumscribed circle: U[66.1; 117.0555095388]
Coordinates of the inscribed circle: I[71.185; 50.78219790897]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.4659669018° = 100°27'35″ = 1.38882406638 rad
∠ B' = β' = 108.9933372445° = 108°59'36″ = 1.23992994416 rad
∠ C' = γ' = 150.5476958537° = 150°32'49″ = 0.51440525483 rad

Calculate another triangle


How did we calculate this triangle?

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

p = a+b+c = 264.39+254.22+132.2 = 650.81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 650.81 }{ 2 } = 325.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 325.41 * (325.41-264.39)(325.41-254.22)(325.41-132.2) } ; ; T = sqrt{ 273066037.47 } = 16524.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16524.71 }{ 264.39 } = 125 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16524.71 }{ 254.22 } = 130 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16524.71 }{ 132.2 } = 250 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 254.22**2+132.2**2-264.39**2 }{ 2 * 254.22 * 132.2 } ) = 79° 32'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 264.39**2+132.2**2-254.22**2 }{ 2 * 264.39 * 132.2 } ) = 71° 24" ; ; gamma = 180° - alpha - beta = 180° - 79° 32'25" - 71° 24" = 29° 27'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16524.71 }{ 325.41 } = 50.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 264.39 }{ 2 * sin 79° 32'25" } = 134.43 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 254.22**2+2 * 132.2**2 - 264.39**2 } }{ 2 } = 153.547 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 132.2**2+2 * 264.39**2 - 254.22**2 } }{ 2 } = 165.929 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 254.22**2+2 * 264.39**2 - 132.2**2 } }{ 2 } = 250.79 ; ;
Calculate another triangle

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

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