Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 6.32   b = 7.21   c = 4.47

Area: T = 13.98550578833
Perimeter: p = 18
Semiperimeter: s = 9

Angle ∠ A = α = 60.21113177853° = 60°12'41″ = 1.05108857423 rad
Angle ∠ B = β = 81.92223619879° = 81°55'20″ = 1.43298149477 rad
Angle ∠ C = γ = 37.86663202268° = 37°51'59″ = 0.66108919636 rad

Height: ha = 4.42656512289
Height: hb = 3.87993503144
Height: hc = 6.25772965921

Median: ma = 5.09987155245
Median: mb = 4.11989349352
Median: mc = 6.40106269224

Inradius: r = 1.55438953204
Circumradius: R = 3.64111251512

Vertex coordinates: A[4.47; 0] B[0; 0] C[0.88880536913; 6.25772965921]
Centroid: CG[1.78660178971; 2.08657655307]
Coordinates of the circumscribed circle: U[2.235; 2.87444681885]
Coordinates of the inscribed circle: I[1.79; 1.55438953204]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 119.7898682215° = 119°47'19″ = 1.05108857423 rad
∠ B' = β' = 98.07876380121° = 98°4'40″ = 1.43298149477 rad
∠ C' = γ' = 142.1343679773° = 142°8'1″ = 0.66108919636 rad

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How did we calculate this triangle?

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

p = a+b+c = 6.32+7.21+4.47 = 18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18 }{ 2 } = 9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9 * (9-6.32)(9-7.21)(9-4.47) } ; ; T = sqrt{ 195.58 } = 13.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.99 }{ 6.32 } = 4.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.99 }{ 7.21 } = 3.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.99 }{ 4.47 } = 6.26 ; ;

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{ 7.21**2+4.47**2-6.32**2 }{ 2 * 7.21 * 4.47 } ) = 60° 12'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.32**2+4.47**2-7.21**2 }{ 2 * 6.32 * 4.47 } ) = 81° 55'20" ; ; gamma = 180° - alpha - beta = 180° - 60° 12'41" - 81° 55'20" = 37° 51'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.99 }{ 9 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.32 }{ 2 * sin 60° 12'41" } = 3.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.21**2+2 * 4.47**2 - 6.32**2 } }{ 2 } = 5.099 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 6.32**2 - 7.21**2 } }{ 2 } = 4.119 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.21**2+2 * 6.32**2 - 4.47**2 } }{ 2 } = 6.401 ; ;
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