Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.62   b = 12.04   c = 6.4

Area: T = 21.51102373188
Perimeter: p = 26.06
Semiperimeter: s = 13.03

Angle ∠ A = α = 33.93884112001° = 33°56'18″ = 0.59223370183 rad
Angle ∠ B = β = 118.0987725985° = 118°5'52″ = 2.06111941576 rad
Angle ∠ C = γ = 27.96438628144° = 27°57'50″ = 0.48880614777 rad

Height: ha = 5.64657315797
Height: hb = 3.57331291227
Height: hc = 6.72219491621

Median: ma = 8.8576901264
Median: mb = 3.64330481743
Median: mc = 9.55436903864

Inradius: r = 1.6510824046
Circumradius: R = 6.82442705938

Vertex coordinates: A[6.4; 0] B[0; 0] C[-3.589884375; 6.72219491621]
Centroid: CG[0.93770520833; 2.24106497207]
Coordinates of the circumscribed circle: U[3.2; 6.02774927737]
Coordinates of the inscribed circle: I[0.99; 1.6510824046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.06215888° = 146°3'42″ = 0.59223370183 rad
∠ B' = β' = 61.90222740146° = 61°54'8″ = 2.06111941576 rad
∠ C' = γ' = 152.0366137186° = 152°2'10″ = 0.48880614777 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 = 7.62+12.04+6.4 = 26.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.06 }{ 2 } = 13.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.03 * (13.03-7.62)(13.03-12.04)(13.03-6.4) } ; ; T = sqrt{ 462.69 } = 21.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.51 }{ 7.62 } = 5.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.51 }{ 12.04 } = 3.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.51 }{ 6.4 } = 6.72 ; ;

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{ 12.04**2+6.4**2-7.62**2 }{ 2 * 12.04 * 6.4 } ) = 33° 56'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.62**2+6.4**2-12.04**2 }{ 2 * 7.62 * 6.4 } ) = 118° 5'52" ; ; gamma = 180° - alpha - beta = 180° - 33° 56'18" - 118° 5'52" = 27° 57'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.51 }{ 13.03 } = 1.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.62 }{ 2 * sin 33° 56'18" } = 6.82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.04**2+2 * 6.4**2 - 7.62**2 } }{ 2 } = 8.857 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 7.62**2 - 12.04**2 } }{ 2 } = 3.643 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.04**2+2 * 7.62**2 - 6.4**2 } }{ 2 } = 9.554 ; ;
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