Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10.41   b = 6.46   c = 14.6

Area: T = 29.69994269429
Perimeter: p = 31.47
Semiperimeter: s = 15.735

Angle ∠ A = α = 39.03443025383° = 39°2'3″ = 0.68112771005 rad
Angle ∠ B = β = 23.00554029601° = 23°19″ = 0.40215200274 rad
Angle ∠ C = γ = 117.9660294502° = 117°57'37″ = 2.05987955257 rad

Height: ha = 5.70659417758
Height: hb = 9.19548690226
Height: hc = 4.06884146497

Median: ma = 10.0187673133
Median: mb = 12.26109604028
Median: mc = 4.66547454379

Inradius: r = 1.88774754968
Circumradius: R = 8.26547180524

Vertex coordinates: A[14.6; 0] B[0; 0] C[9.58220719178; 4.06884146497]
Centroid: CG[8.06106906393; 1.35661382166]
Coordinates of the circumscribed circle: U[7.3; -3.87549921916]
Coordinates of the inscribed circle: I[9.275; 1.88774754968]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.9665697462° = 140°57'57″ = 0.68112771005 rad
∠ B' = β' = 156.995459704° = 156°59'41″ = 0.40215200274 rad
∠ C' = γ' = 62.04397054984° = 62°2'23″ = 2.05987955257 rad

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How did we calculate this triangle?

a = 10.41 ; ; b = 6.46 ; ; c = 14.6 ; ;

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

p = a+b+c = 10.41+6.46+14.6 = 31.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.47 }{ 2 } = 15.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.74 * (15.74-10.41)(15.74-6.46)(15.74-14.6) } ; ; T = sqrt{ 882.06 } = 29.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.7 }{ 10.41 } = 5.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.7 }{ 6.46 } = 9.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.7 }{ 14.6 } = 4.07 ; ;

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{ 6.46**2+14.6**2-10.41**2 }{ 2 * 6.46 * 14.6 } ) = 39° 2'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.41**2+14.6**2-6.46**2 }{ 2 * 10.41 * 14.6 } ) = 23° 19" ; ; gamma = 180° - alpha - beta = 180° - 39° 2'3" - 23° 19" = 117° 57'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.7 }{ 15.74 } = 1.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.41 }{ 2 * sin 39° 2'3" } = 8.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.46**2+2 * 14.6**2 - 10.41**2 } }{ 2 } = 10.018 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.6**2+2 * 10.41**2 - 6.46**2 } }{ 2 } = 12.261 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.46**2+2 * 10.41**2 - 14.6**2 } }{ 2 } = 4.665 ; ;
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