Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 12.17   b = 12.53   c = 10.82

Area: T = 60.02985653842
Perimeter: p = 35.52
Semiperimeter: s = 17.76

Angle ∠ A = α = 62.31884107128° = 62°19'6″ = 1.08876614515 rad
Angle ∠ B = β = 65.74766651458° = 65°44'48″ = 1.1477495779 rad
Angle ∠ C = γ = 51.93549241414° = 51°56'6″ = 0.9066435423 rad

Height: ha = 9.86550066367
Height: hb = 9.58215746822
Height: hc = 11.09658531209

Median: ma = 100.0004712389
Median: mb = 9.66112848524
Median: mc = 11.10334589205

Inradius: r = 3.38799867896
Circumradius: R = 6.87114905622

Vertex coordinates: A[10.82; 0] B[0; 0] C[4.99990942699; 11.09658531209]
Centroid: CG[5.27330314233; 3.6998617707]
Coordinates of the circumscribed circle: U[5.41; 4.23766593616]
Coordinates of the inscribed circle: I[5.23; 3.38799867896]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.6821589287° = 117°40'54″ = 1.08876614515 rad
∠ B' = β' = 114.2533334854° = 114°15'12″ = 1.1477495779 rad
∠ C' = γ' = 128.0655075859° = 128°3'54″ = 0.9066435423 rad

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How did we calculate this triangle?

a = 12.17 ; ; b = 12.53 ; ; c = 10.82 ; ;

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

p = a+b+c = 12.17+12.53+10.82 = 35.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.52 }{ 2 } = 17.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.76 * (17.76-12.17)(17.76-12.53)(17.76-10.82) } ; ; T = sqrt{ 3603.43 } = 60.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60.03 }{ 12.17 } = 9.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60.03 }{ 12.53 } = 9.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60.03 }{ 10.82 } = 11.1 ; ;

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{ 12.53**2+10.82**2-12.17**2 }{ 2 * 12.53 * 10.82 } ) = 62° 19'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.17**2+10.82**2-12.53**2 }{ 2 * 12.17 * 10.82 } ) = 65° 44'48" ; ; gamma = 180° - alpha - beta = 180° - 62° 19'6" - 65° 44'48" = 51° 56'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60.03 }{ 17.76 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.17 }{ 2 * sin 62° 19'6" } = 6.87 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.53**2+2 * 10.82**2 - 12.17**2 } }{ 2 } = 10 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.82**2+2 * 12.17**2 - 12.53**2 } }{ 2 } = 9.661 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.53**2+2 * 12.17**2 - 10.82**2 } }{ 2 } = 11.103 ; ;
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