Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 162   b = 125   c = 54.95

Area: T = 2861.015537917
Perimeter: p = 341.95
Semiperimeter: s = 170.975

Angle ∠ A = α = 123.5866386456° = 123°35'11″ = 2.15769893543 rad
Angle ∠ B = β = 409.9999977791° = 40° = 0.6988131662 rad
Angle ∠ C = γ = 16.41436157645° = 16°24'49″ = 0.28664716372 rad

Height: ha = 35.32111775206
Height: hb = 45.77662460667
Height: hc = 104.1321587959

Median: ma = 52.54876093652
Median: mb = 103.5643995916
Median: mc = 142.0555004752

Inradius: r = 16.73435305113
Circumradius: R = 97.23327436705

Vertex coordinates: A[54.95; 0] B[0; 0] C[124.0999203822; 104.1321587959]
Centroid: CG[59.68330679406; 34.71105293196]
Coordinates of the circumscribed circle: U[27.475; 93.27702032628]
Coordinates of the inscribed circle: I[45.975; 16.73435305113]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 56.41436135436° = 56°24'49″ = 2.15769893543 rad
∠ B' = β' = 1400.000002221° = 140° = 0.6988131662 rad
∠ C' = γ' = 163.5866384236° = 163°35'11″ = 0.28664716372 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 = 162+125+54.95 = 341.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 341.95 }{ 2 } = 170.98 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 170.98 * (170.98-162)(170.98-125)(170.98-54.95) } ; ; T = sqrt{ 8185409 } = 2861.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2861.02 }{ 162 } = 35.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2861.02 }{ 125 } = 45.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2861.02 }{ 54.95 } = 104.13 ; ;

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{ 125**2+54.95**2-162**2 }{ 2 * 125 * 54.95 } ) = 123° 35'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 162**2+54.95**2-125**2 }{ 2 * 162 * 54.95 } ) = 40° ; ; gamma = 180° - alpha - beta = 180° - 123° 35'11" - 40° = 16° 24'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2861.02 }{ 170.98 } = 16.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 162 }{ 2 * sin 123° 35'11" } = 97.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 54.95**2 - 162**2 } }{ 2 } = 52.548 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 54.95**2+2 * 162**2 - 125**2 } }{ 2 } = 103.564 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 162**2 - 54.95**2 } }{ 2 } = 142.055 ; ;
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