Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37   b = 34   c = 3.26

Area: T = 22.62111103262
Perimeter: p = 74.26
Semiperimeter: s = 37.13

Angle ∠ A = α = 155.9109698704° = 155°54'35″ = 2.72111375782 rad
Angle ∠ B = β = 22.02992938194° = 22°1'45″ = 0.3844483709 rad
Angle ∠ C = γ = 2.06110074769° = 2°3'40″ = 0.03659713664 rad

Height: ha = 1.22327627203
Height: hb = 1.33106535486
Height: hc = 13.87879817952

Median: ma = 15.52662294199
Median: mb = 20.02203346625
Median: mc = 35.49442685514

Inradius: r = 0.60992407844
Circumradius: R = 45.32435931047

Vertex coordinates: A[3.26; 0] B[0; 0] C[34.29987116564; 13.87879817952]
Centroid: CG[12.52195705521; 4.62659939317]
Coordinates of the circumscribed circle: U[1.63; 45.29442732795]
Coordinates of the inscribed circle: I[3.13; 0.60992407844]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 24.09903012963° = 24°5'25″ = 2.72111375782 rad
∠ B' = β' = 157.9710706181° = 157°58'15″ = 0.3844483709 rad
∠ C' = γ' = 177.9398992523° = 177°56'20″ = 0.03659713664 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 = 37+34+3.26 = 74.26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74.26 }{ 2 } = 37.13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.13 * (37.13-37)(37.13-34)(37.13-3.26) } ; ; T = sqrt{ 511.71 } = 22.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.62 }{ 37 } = 1.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.62 }{ 34 } = 1.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.62 }{ 3.26 } = 13.88 ; ;

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{ 34**2+3.26**2-37**2 }{ 2 * 34 * 3.26 } ) = 155° 54'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37**2+3.26**2-34**2 }{ 2 * 37 * 3.26 } ) = 22° 1'45" ; ;
gamma = 180° - alpha - beta = 180° - 155° 54'35" - 22° 1'45" = 2° 3'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.62 }{ 37.13 } = 0.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37 }{ 2 * sin 155° 54'35" } = 45.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 3.26**2 - 37**2 } }{ 2 } = 15.526 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.26**2+2 * 37**2 - 34**2 } }{ 2 } = 20.02 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 37**2 - 3.26**2 } }{ 2 } = 35.494 ; ;
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