Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37.3   b = 29.8   c = 9.88

Area: T = 106.7132735626
Perimeter: p = 76.98
Semiperimeter: s = 38.49

Angle ∠ A = α = 133.5440172747° = 133°32'25″ = 2.33107156981 rad
Angle ∠ B = β = 35.39897880085° = 35°23'23″ = 0.61876683223 rad
Angle ∠ C = γ = 11.07700392447° = 11°4'12″ = 0.19332086331 rad

Height: ha = 5.72218625001
Height: hb = 7.16219285655
Height: hc = 21.60217683453

Median: ma = 12.04217897341
Median: mb = 22.85769945531
Median: mc = 33.3965529641

Inradius: r = 2.77224794915
Circumradius: R = 25.72879862979

Vertex coordinates: A[9.88; 0] B[0; 0] C[30.40881174089; 21.60217683453]
Centroid: CG[13.42993724696; 7.20105894484]
Coordinates of the circumscribed circle: U[4.94; 25.24992708597]
Coordinates of the inscribed circle: I[8.69; 2.77224794915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 46.46598272533° = 46°27'35″ = 2.33107156981 rad
∠ B' = β' = 144.6110211991° = 144°36'37″ = 0.61876683223 rad
∠ C' = γ' = 168.9329960755° = 168°55'48″ = 0.19332086331 rad

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How did we calculate this triangle?

a = 37.3 ; ; b = 29.8 ; ; c = 9.88 ; ;

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

p = a+b+c = 37.3+29.8+9.88 = 76.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76.98 }{ 2 } = 38.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.49 * (38.49-37.3)(38.49-29.8)(38.49-9.88) } ; ; T = sqrt{ 11387.61 } = 106.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106.71 }{ 37.3 } = 5.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106.71 }{ 29.8 } = 7.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106.71 }{ 9.88 } = 21.6 ; ;

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{ 29.8**2+9.88**2-37.3**2 }{ 2 * 29.8 * 9.88 } ) = 133° 32'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.3**2+9.88**2-29.8**2 }{ 2 * 37.3 * 9.88 } ) = 35° 23'23" ; ; gamma = 180° - alpha - beta = 180° - 133° 32'25" - 35° 23'23" = 11° 4'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106.71 }{ 38.49 } = 2.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37.3 }{ 2 * sin 133° 32'25" } = 25.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.8**2+2 * 9.88**2 - 37.3**2 } }{ 2 } = 12.042 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.88**2+2 * 37.3**2 - 29.8**2 } }{ 2 } = 22.857 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.8**2+2 * 37.3**2 - 9.88**2 } }{ 2 } = 33.396 ; ;
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