Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.5   b = 5.82   c = 10.33

Area: T = 11.95502887459
Perimeter: p = 21.65
Semiperimeter: s = 10.825

Angle ∠ A = α = 23.42547250143° = 23°25'29″ = 0.40988385779 rad
Angle ∠ B = β = 24.87771296547° = 24°52'38″ = 0.43441878209 rad
Angle ∠ C = γ = 131.6988145331° = 131°41'53″ = 2.29985662548 rad

Height: ha = 4.34655595439
Height: hb = 4.1076628435
Height: hc = 2.31437054687

Median: ma = 7.9220110479
Median: mb = 7.74766992971
Median: mc = 2.32203394148

Inradius: r = 1.1043952771
Circumradius: R = 6.91774751136

Vertex coordinates: A[10.33; 0] B[0; 0] C[4.99896660213; 2.31437054687]
Centroid: CG[5.10765553404; 0.77112351562]
Coordinates of the circumscribed circle: U[5.165; -4.60215472341]
Coordinates of the inscribed circle: I[5.005; 1.1043952771]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.5755274986° = 156°34'31″ = 0.40988385779 rad
∠ B' = β' = 155.1232870345° = 155°7'22″ = 0.43441878209 rad
∠ C' = γ' = 48.30218546691° = 48°18'7″ = 2.29985662548 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 = 5.5+5.82+10.33 = 21.65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.65 }{ 2 } = 10.83 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.83 * (10.83-5.5)(10.83-5.82)(10.83-10.33) } ; ; T = sqrt{ 142.81 } = 11.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.95 }{ 5.5 } = 4.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.95 }{ 5.82 } = 4.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.95 }{ 10.33 } = 2.31 ; ;

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{ 5.82**2+10.33**2-5.5**2 }{ 2 * 5.82 * 10.33 } ) = 23° 25'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.5**2+10.33**2-5.82**2 }{ 2 * 5.5 * 10.33 } ) = 24° 52'38" ; ; gamma = 180° - alpha - beta = 180° - 23° 25'29" - 24° 52'38" = 131° 41'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.95 }{ 10.83 } = 1.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.5 }{ 2 * sin 23° 25'29" } = 6.92 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.82**2+2 * 10.33**2 - 5.5**2 } }{ 2 } = 7.92 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.33**2+2 * 5.5**2 - 5.82**2 } }{ 2 } = 7.747 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.82**2+2 * 5.5**2 - 10.33**2 } }{ 2 } = 2.32 ; ;
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