Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 50   b = 70   c = 62.45

Area: T = 1515.545481747
Perimeter: p = 182.45
Semiperimeter: s = 91.225

Angle ∠ A = α = 43.89878817041° = 43°53'52″ = 0.76661625704 rad
Angle ∠ B = β = 76.10220946675° = 76°6'8″ = 1.32882321196 rad
Angle ∠ C = γ = 600.0000236284° = 60° = 1.04771979636 rad

Height: ha = 60.62217926987
Height: hb = 43.3011280499
Height: hc = 48.53662631695

Median: ma = 61.44110388096
Median: mb = 44.44109861502
Median: mc = 52.20215265581

Inradius: r = 16.6133261907
Circumradius: R = 36.05655157262

Vertex coordinates: A[62.45; 0] B[0; 0] C[12.01096277022; 48.53662631695]
Centroid: CG[24.82198759007; 16.17987543898]
Coordinates of the circumscribed circle: U[31.225; 18.02877449862]
Coordinates of the inscribed circle: I[21.225; 16.6133261907]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.1022118296° = 136°6'8″ = 0.76661625704 rad
∠ B' = β' = 103.8987905332° = 103°53'52″ = 1.32882321196 rad
∠ C' = γ' = 1209.999976372° = 120° = 1.04771979636 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 = 50+70+62.45 = 182.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 182.45 }{ 2 } = 91.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 91.23 * (91.23-50)(91.23-70)(91.23-62.45) } ; ; T = sqrt{ 2296876.09 } = 1515.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1515.54 }{ 50 } = 60.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1515.54 }{ 70 } = 43.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1515.54 }{ 62.45 } = 48.54 ; ;

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{ 70**2+62.45**2-50**2 }{ 2 * 70 * 62.45 } ) = 43° 53'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+62.45**2-70**2 }{ 2 * 50 * 62.45 } ) = 76° 6'8" ; ; gamma = 180° - alpha - beta = 180° - 43° 53'52" - 76° 6'8" = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1515.54 }{ 91.23 } = 16.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 50 }{ 2 * sin 43° 53'52" } = 36.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 62.45**2 - 50**2 } }{ 2 } = 61.441 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 62.45**2+2 * 50**2 - 70**2 } }{ 2 } = 44.441 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 50**2 - 62.45**2 } }{ 2 } = 52.202 ; ;
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