Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6.32   b = 9.22   c = 15.52

Area: T = 3.00442095516
Perimeter: p = 31.06
Semiperimeter: s = 15.53

Angle ∠ A = α = 2.40765113381° = 2°24'23″ = 0.04220015463 rad
Angle ∠ B = β = 3.51219314784° = 3°30'43″ = 0.06112947674 rad
Angle ∠ C = γ = 174.0821557183° = 174°4'54″ = 3.03882963399 rad

Height: ha = 0.95106992252
Height: hb = 0.65216723539
Height: hc = 0.38771404061

Median: ma = 12.36774492115
Median: mb = 10.91657821525
Median: mc = 1.50325977506

Inradius: r = 0.19334455603
Circumradius: R = 75.25774506258

Vertex coordinates: A[15.52; 0] B[0; 0] C[6.30881314433; 0.38771404061]
Centroid: CG[7.27660438144; 0.1299046802]
Coordinates of the circumscribed circle: U[7.76; -74.85663041747]
Coordinates of the inscribed circle: I[6.31; 0.19334455603]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.5933488662° = 177°35'37″ = 0.04220015463 rad
∠ B' = β' = 176.4888068522° = 176°29'17″ = 0.06112947674 rad
∠ C' = γ' = 5.91884428165° = 5°55'6″ = 3.03882963399 rad

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How did we calculate this triangle?

a = 6.32 ; ; b = 9.22 ; ; c = 15.52 ; ;

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

p = a+b+c = 6.32+9.22+15.52 = 31.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.06 }{ 2 } = 15.53 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.53 * (15.53-6.32)(15.53-9.22)(15.53-15.52) } ; ; T = sqrt{ 9.03 } = 3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3 }{ 6.32 } = 0.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3 }{ 9.22 } = 0.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3 }{ 15.52 } = 0.39 ; ;

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{ 9.22**2+15.52**2-6.32**2 }{ 2 * 9.22 * 15.52 } ) = 2° 24'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.32**2+15.52**2-9.22**2 }{ 2 * 6.32 * 15.52 } ) = 3° 30'43" ; ; gamma = 180° - alpha - beta = 180° - 2° 24'23" - 3° 30'43" = 174° 4'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3 }{ 15.53 } = 0.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.32 }{ 2 * sin 2° 24'23" } = 75.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.22**2+2 * 15.52**2 - 6.32**2 } }{ 2 } = 12.367 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.52**2+2 * 6.32**2 - 9.22**2 } }{ 2 } = 10.916 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.22**2+2 * 6.32**2 - 15.52**2 } }{ 2 } = 1.503 ; ;
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