Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10.2   b = 5.66   c = 6.32

Area: T = 15.98989476549
Perimeter: p = 22.18
Semiperimeter: s = 11.09

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

Height: ha = 3.13550877755
Height: hb = 5.6549804825
Height: hc = 5.06597935617

Median: ma = 3.15989555236
Median: mb = 7.99988936735
Median: mc = 7.6199199433

Inradius: r = 1.44217446037
Circumradius: R = 5.70549758351

Vertex coordinates: A[6.32; 0] B[0; 0] C[8.85765506329; 5.06597935617]
Centroid: CG[5.0598850211; 1.68765978539]
Coordinates of the circumscribed circle: U[3.16; 4.75498578167]
Coordinates of the inscribed circle: I[5.43; 1.44217446037]

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

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How did we calculate this triangle?

a = 10.2 ; ; b = 5.66 ; ; c = 6.32 ; ;

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

p = a+b+c = 10.2+5.66+6.32 = 22.18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.18 }{ 2 } = 11.09 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.09 * (11.09-10.2)(11.09-5.66)(11.09-6.32) } ; ; T = sqrt{ 255.65 } = 15.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.99 }{ 10.2 } = 3.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.99 }{ 5.66 } = 5.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.99 }{ 6.32 } = 5.06 ; ;

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{ 5.66**2+6.32**2-10.2**2 }{ 2 * 5.66 * 6.32 } ) = 116° 37'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.2**2+6.32**2-5.66**2 }{ 2 * 10.2 * 6.32 } ) = 29° 44'22" ; ; gamma = 180° - alpha - beta = 180° - 116° 37'31" - 29° 44'22" = 33° 38'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.99 }{ 11.09 } = 1.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.2 }{ 2 * sin 116° 37'31" } = 5.7 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 6.32**2 - 10.2**2 } }{ 2 } = 3.159 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 10.2**2 - 5.66**2 } }{ 2 } = 7.999 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 10.2**2 - 6.32**2 } }{ 2 } = 7.619 ; ;
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