Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 15.8   b = 43.72   c = 41.36

Area: T = 326.5165679642
Perimeter: p = 100.88
Semiperimeter: s = 50.44

Angle ∠ A = α = 21.17701093913° = 21°10'12″ = 0.36994881119 rad
Angle ∠ B = β = 87.85879409909° = 87°51'29″ = 1.53334103443 rad
Angle ∠ C = γ = 70.97219496177° = 70°58'19″ = 1.23986941974 rad

Height: ha = 41.33110986889
Height: hb = 14.93766733597
Height: hc = 15.78989593637

Median: ma = 41.81766713166
Median: mb = 22.41217201482
Median: mc = 25.55114539704

Inradius: r = 6.47333481293
Circumradius: R = 21.87552858908

Vertex coordinates: A[41.36; 0] B[0; 0] C[0.59105609284; 15.78989593637]
Centroid: CG[13.98435203095; 5.26329864546]
Coordinates of the circumscribed circle: U[20.68; 7.13220216492]
Coordinates of the inscribed circle: I[6.72; 6.47333481293]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8329890609° = 158°49'48″ = 0.36994881119 rad
∠ B' = β' = 92.14220590091° = 92°8'31″ = 1.53334103443 rad
∠ C' = γ' = 109.0288050382° = 109°1'41″ = 1.23986941974 rad

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How did we calculate this triangle?

a = 15.8 ; ; b = 43.72 ; ; c = 41.36 ; ;

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

p = a+b+c = 15.8+43.72+41.36 = 100.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 100.88 }{ 2 } = 50.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.44 * (50.44-15.8)(50.44-43.72)(50.44-41.36) } ; ; T = sqrt{ 106612.49 } = 326.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 326.52 }{ 15.8 } = 41.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 326.52 }{ 43.72 } = 14.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 326.52 }{ 41.36 } = 15.79 ; ;

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{ 43.72**2+41.36**2-15.8**2 }{ 2 * 43.72 * 41.36 } ) = 21° 10'12" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15.8**2+41.36**2-43.72**2 }{ 2 * 15.8 * 41.36 } ) = 87° 51'29" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 15.8**2+43.72**2-41.36**2 }{ 2 * 15.8 * 43.72 } ) = 70° 58'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 326.52 }{ 50.44 } = 6.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15.8 }{ 2 * sin 21° 10'12" } = 21.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.72**2+2 * 41.36**2 - 15.8**2 } }{ 2 } = 41.817 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 41.36**2+2 * 15.8**2 - 43.72**2 } }{ 2 } = 22.412 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.72**2+2 * 15.8**2 - 41.36**2 } }{ 2 } = 25.551 ; ;
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