Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.83   b = 5.1   c = 3.16

Area: T = 3.99772369137
Perimeter: p = 11.09
Semiperimeter: s = 5.545

Angle ∠ A = α = 29.7439552969° = 29°44'22″ = 0.51990531174 rad
Angle ∠ B = β = 116.625529665° = 116°37'31″ = 2.03554954177 rad
Angle ∠ C = γ = 33.63551503812° = 33°38'7″ = 0.58770441186 rad

Height: ha = 2.82549024125
Height: hb = 1.56875438877
Height: hc = 2.53298967808

Median: ma = 3.99994468368
Median: mb = 1.57994777618
Median: mc = 3.81095997165

Inradius: r = 0.72108723018
Circumradius: R = 2.85224879176

Vertex coordinates: A[3.16; 0] B[0; 0] C[-1.26882753165; 2.53298967808]
Centroid: CG[0.63105748945; 0.84332989269]
Coordinates of the circumscribed circle: U[1.58; 2.37549289084]
Coordinates of the inscribed circle: I[0.445; 0.72108723018]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2660447031° = 150°15'38″ = 0.51990531174 rad
∠ B' = β' = 63.37547033502° = 63°22'29″ = 2.03554954177 rad
∠ C' = γ' = 146.3654849619° = 146°21'53″ = 0.58770441186 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 = 2.83+5.1+3.16 = 11.09 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.09 }{ 2 } = 5.55 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.55 * (5.55-2.83)(5.55-5.1)(5.55-3.16) } ; ; T = sqrt{ 15.98 } = 4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4 }{ 2.83 } = 2.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4 }{ 5.1 } = 1.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4 }{ 3.16 } = 2.53 ; ;

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{ 5.1**2+3.16**2-2.83**2 }{ 2 * 5.1 * 3.16 } ) = 29° 44'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.83**2+3.16**2-5.1**2 }{ 2 * 2.83 * 3.16 } ) = 116° 37'31" ; ; gamma = 180° - alpha - beta = 180° - 29° 44'22" - 116° 37'31" = 33° 38'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4 }{ 5.55 } = 0.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.83 }{ 2 * sin 29° 44'22" } = 2.85 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 3.16**2 - 2.83**2 } }{ 2 } = 3.999 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 2.83**2 - 5.1**2 } }{ 2 } = 1.579 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 2.83**2 - 3.16**2 } }{ 2 } = 3.81 ; ;
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