Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 152.12   b = 124   c = 164

Area: T = 8972.866561486
Perimeter: p = 440.12
Semiperimeter: s = 220.06

Angle ∠ A = α = 61.94106983987° = 61°56'27″ = 1.0811069128 rad
Angle ∠ B = β = 465.9995770789° = 45°59'58″ = 0.80328440746 rad
Angle ∠ C = γ = 72.06597245224° = 72°3'35″ = 1.2587679451 rad

Height: ha = 117.9710886338
Height: hb = 144.7243638949
Height: hc = 109.4255190425

Median: ma = 123.8998653746
Median: mb = 145.5143735434
Median: mc = 111.9566452248

Inradius: r = 40.77546324405
Circumradius: R = 86.19107570218

Vertex coordinates: A[164; 0] B[0; 0] C[105.6722239024; 109.4255190425]
Centroid: CG[89.89107463415; 36.4755063475]
Coordinates of the circumscribed circle: U[82; 26.54989471731]
Coordinates of the inscribed circle: I[96.06; 40.77546324405]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.0599301601° = 118°3'33″ = 1.0811069128 rad
∠ B' = β' = 1344.000422921° = 134°2″ = 0.80328440746 rad
∠ C' = γ' = 107.9440275478° = 107°56'25″ = 1.2587679451 rad

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How did we calculate this triangle?

a = 152.12 ; ; b = 124 ; ; c = 164 ; ;

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

p = a+b+c = 152.12+124+164 = 440.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 440.12 }{ 2 } = 220.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 220.06 * (220.06-152.12)(220.06-124)(220.06-164) } ; ; T = sqrt{ 80512317.34 } = 8972.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8972.87 }{ 152.12 } = 117.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8972.87 }{ 124 } = 144.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8972.87 }{ 164 } = 109.43 ; ;

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{ 124**2+164**2-152.12**2 }{ 2 * 124 * 164 } ) = 61° 56'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 152.12**2+164**2-124**2 }{ 2 * 152.12 * 164 } ) = 45° 59'58" ; ; gamma = 180° - alpha - beta = 180° - 61° 56'27" - 45° 59'58" = 72° 3'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8972.87 }{ 220.06 } = 40.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 152.12 }{ 2 * sin 61° 56'27" } = 86.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 124**2+2 * 164**2 - 152.12**2 } }{ 2 } = 123.899 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 164**2+2 * 152.12**2 - 124**2 } }{ 2 } = 145.514 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 124**2+2 * 152.12**2 - 164**2 } }{ 2 } = 111.956 ; ;
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