Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 242.2   b = 186.2   c = 311.99

Area: T = 22526.56330028
Perimeter: p = 740.39
Semiperimeter: s = 370.195

Angle ∠ A = α = 50.8544077579° = 50°51'15″ = 0.88875710918 rad
Angle ∠ B = β = 36.66000025223° = 36°36' = 0.63987905503 rad
Angle ∠ C = γ = 92.54659198986° = 92°32'45″ = 1.61552310115 rad

Height: ha = 186.0166209767
Height: hb = 241.9610934509
Height: hc = 144.4065673277

Median: ma = 226.5810868676
Median: mb = 263.3099115015
Median: mc = 149.436627396

Inradius: r = 60.85105328348
Circumradius: R = 156.1499128274

Vertex coordinates: A[311.99; 0] B[0; 0] C[194.4422386134; 144.4065673277]
Centroid: CG[168.8110795378; 48.13552244255]
Coordinates of the circumscribed circle: U[155.995; -6.9366154254]
Coordinates of the inscribed circle: I[183.995; 60.85105328348]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.1465922421° = 129°8'45″ = 0.88875710918 rad
∠ B' = β' = 143.4399997478° = 143°24' = 0.63987905503 rad
∠ C' = γ' = 87.45440801014° = 87°27'15″ = 1.61552310115 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+311.99 = 740.39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 740.39 }{ 2 } = 370.2 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 370.2 * (370.2-242.2)(370.2-186.2)(370.2-311.99) } ; ; T = sqrt{ 507446040.72 } = 22526.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22526.56 }{ 242.2 } = 186.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22526.56 }{ 186.2 } = 241.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22526.56 }{ 311.99 } = 144.41 ; ;

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+311.99**2-242.2**2 }{ 2 * 186.2 * 311.99 } ) = 50° 51'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 242.2**2+311.99**2-186.2**2 }{ 2 * 242.2 * 311.99 } ) = 36° 36' ; ; gamma = 180° - alpha - beta = 180° - 50° 51'15" - 36° 36' = 92° 32'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22526.56 }{ 370.2 } = 60.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 242.2 }{ 2 * sin 50° 51'15" } = 156.15 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 186.2**2+2 * 311.99**2 - 242.2**2 } }{ 2 } = 226.581 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 311.99**2+2 * 242.2**2 - 186.2**2 } }{ 2 } = 263.309 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 186.2**2+2 * 242.2**2 - 311.99**2 } }{ 2 } = 149.436 ; ;
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