Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 242.2   b = 186.2   c = 76.89

Area: T = 5551.298840902
Perimeter: p = 505.29
Semiperimeter: s = 252.645

Angle ∠ A = α = 129.1510710858° = 129°9'3″ = 2.25441051358 rad
Angle ∠ B = β = 36.59771076409° = 36°35'50″ = 0.6398740025 rad
Angle ∠ C = γ = 14.25221815014° = 14°15'8″ = 0.24987474928 rad

Height: ha = 45.84106144427
Height: hb = 59.6277265403
Height: hc = 144.3965848849

Median: ma = 75.00769733425
Median: mb = 153.6844241385
Median: mc = 212.5743803595

Inradius: r = 21.97327222348
Circumradius: R = 156.1659752373

Vertex coordinates: A[76.89; 0] B[0; 0] C[194.4549682013; 144.3965848849]
Centroid: CG[90.44765606711; 48.13219496165]
Coordinates of the circumscribed circle: U[38.445; 151.3533395192]
Coordinates of the inscribed circle: I[66.445; 21.97327222348]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 50.84992891423° = 50°50'57″ = 2.25441051358 rad
∠ B' = β' = 143.4032892359° = 143°24'10″ = 0.6398740025 rad
∠ C' = γ' = 165.7487818499° = 165°44'52″ = 0.24987474928 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 = 242.2+186.2+76.89 = 505.29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 505.29 }{ 2 } = 252.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 252.65 * (252.65-242.2)(252.65-186.2)(252.65-76.89) } ; ; T = sqrt{ 30816914.03 } = 5551.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5551.3 }{ 242.2 } = 45.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5551.3 }{ 186.2 } = 59.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5551.3 }{ 76.89 } = 144.4 ; ;

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{ 186.2**2+76.89**2-242.2**2 }{ 2 * 186.2 * 76.89 } ) = 129° 9'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 242.2**2+76.89**2-186.2**2 }{ 2 * 242.2 * 76.89 } ) = 36° 35'50" ; ; gamma = 180° - alpha - beta = 180° - 129° 9'3" - 36° 35'50" = 14° 15'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5551.3 }{ 252.65 } = 21.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 242.2 }{ 2 * sin 129° 9'3" } = 156.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 186.2**2+2 * 76.89**2 - 242.2**2 } }{ 2 } = 75.007 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 76.89**2+2 * 242.2**2 - 186.2**2 } }{ 2 } = 153.684 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 186.2**2+2 * 242.2**2 - 76.89**2 } }{ 2 } = 212.574 ; ;
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