Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 59   b = 40   c = 32.48

Area: T = 615.9899982665
Perimeter: p = 131.48
Semiperimeter: s = 65.74

Angle ∠ A = α = 108.5366397432° = 108°32'11″ = 1.89443174934 rad
Angle ∠ B = β = 40.00105157131° = 40°2″ = 0.69881407017 rad
Angle ∠ C = γ = 31.46330868553° = 31°27'47″ = 0.54991344585 rad

Height: ha = 20.87879655141
Height: hb = 30.79549991332
Height: hc = 37.92548757798

Median: ma = 21.38328248835
Median: mb = 43.22200786672
Median: mc = 47.71554314661

Inradius: r = 9.36987250177
Circumradius: R = 31.11441427819

Vertex coordinates: A[32.48; 0] B[0; 0] C[45.19662807882; 37.92548757798]
Centroid: CG[25.89220935961; 12.64216252599]
Coordinates of the circumscribed circle: U[16.24; 26.54396360384]
Coordinates of the inscribed circle: I[25.74; 9.36987250177]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 71.46436025684° = 71°27'49″ = 1.89443174934 rad
∠ B' = β' = 139.9999484287° = 139°59'58″ = 0.69881407017 rad
∠ C' = γ' = 148.5376913145° = 148°32'13″ = 0.54991344585 rad

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How did we calculate this triangle?

a = 59 ; ; b = 40 ; ; c = 32.48 ; ;

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

p = a+b+c = 59+40+32.48 = 131.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 131.48 }{ 2 } = 65.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.74 * (65.74-59)(65.74-40)(65.74-32.48) } ; ; T = sqrt{ 379332.79 } = 615.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 615.9 }{ 59 } = 20.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 615.9 }{ 40 } = 30.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 615.9 }{ 32.48 } = 37.92 ; ;

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{ 40**2+32.48**2-59**2 }{ 2 * 40 * 32.48 } ) = 108° 32'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 59**2+32.48**2-40**2 }{ 2 * 59 * 32.48 } ) = 40° 2" ; ; gamma = 180° - alpha - beta = 180° - 108° 32'11" - 40° 2" = 31° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 615.9 }{ 65.74 } = 9.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 59 }{ 2 * sin 108° 32'11" } = 31.11 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 32.48**2 - 59**2 } }{ 2 } = 21.383 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 32.48**2+2 * 59**2 - 40**2 } }{ 2 } = 43.22 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 59**2 - 32.48**2 } }{ 2 } = 47.715 ; ;
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