Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 5.1   b = 4.47   c = 3.16

Area: T = 6.99329929568
Perimeter: p = 12.73
Semiperimeter: s = 6.365

Angle ∠ A = α = 81.94991959775° = 81°56'57″ = 1.43302832892 rad
Angle ∠ B = β = 60.20877116627° = 60°12'28″ = 1.05108228036 rad
Angle ∠ C = γ = 37.84330923598° = 37°50'35″ = 0.66604865608 rad

Height: ha = 2.74223501792
Height: hb = 3.12988559091
Height: hc = 4.42659449094

Median: ma = 2.91221727284
Median: mb = 3.6065908346
Median: mc = 4.52875876579

Inradius: r = 1.09986634653
Circumradius: R = 2.57553822592

Vertex coordinates: A[3.16; 0] B[0; 0] C[2.5343971519; 4.42659449094]
Centroid: CG[1.89879905063; 1.47553149698]
Coordinates of the circumscribed circle: U[1.58; 2.03437634526]
Coordinates of the inscribed circle: I[1.895; 1.09986634653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.05108040225° = 98°3'3″ = 1.43302832892 rad
∠ B' = β' = 119.7922288337° = 119°47'32″ = 1.05108228036 rad
∠ C' = γ' = 142.157690764° = 142°9'25″ = 0.66604865608 rad

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How did we calculate this triangle?

a = 5.1 ; ; b = 4.47 ; ; c = 3.16 ; ;

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

p = a+b+c = 5.1+4.47+3.16 = 12.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.73 }{ 2 } = 6.37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.37 * (6.37-5.1)(6.37-4.47)(6.37-3.16) } ; ; T = sqrt{ 48.9 } = 6.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.99 }{ 5.1 } = 2.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.99 }{ 4.47 } = 3.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.99 }{ 3.16 } = 4.43 ; ;

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{ 4.47**2+3.16**2-5.1**2 }{ 2 * 4.47 * 3.16 } ) = 81° 56'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.1**2+3.16**2-4.47**2 }{ 2 * 5.1 * 3.16 } ) = 60° 12'28" ; ; gamma = 180° - alpha - beta = 180° - 81° 56'57" - 60° 12'28" = 37° 50'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.99 }{ 6.37 } = 1.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.1 }{ 2 * sin 81° 56'57" } = 2.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 3.16**2 - 5.1**2 } }{ 2 } = 2.912 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 5.1**2 - 4.47**2 } }{ 2 } = 3.606 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 5.1**2 - 3.16**2 } }{ 2 } = 4.528 ; ;
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