Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.3   b = 1.8   c = 0.56

Area: T = 0.25660726264
Perimeter: p = 4.66
Semiperimeter: s = 2.33

Angle ∠ A = α = 149.464393563° = 149°27'50″ = 2.60986377897 rad
Angle ∠ B = β = 23.43299956613° = 23°25'48″ = 0.4098930568 rad
Angle ∠ C = γ = 7.10660687092° = 7°6'22″ = 0.12440242958 rad

Height: ha = 0.22326718491
Height: hb = 0.28545251405
Height: hc = 0.91545450943

Median: ma = 0.67440178039
Median: mb = 1.41113114468
Median: mc = 2.04661182762

Inradius: r = 0.11099024148
Circumradius: R = 2.26334203746

Vertex coordinates: A[0.56; 0] B[0; 0] C[2.11103571429; 0.91545450943]
Centroid: CG[0.89901190476; 0.30548483648]
Coordinates of the circumscribed circle: U[0.28; 2.24660346818]
Coordinates of the inscribed circle: I[0.53; 0.11099024148]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.53660643704° = 30°32'10″ = 2.60986377897 rad
∠ B' = β' = 156.5770004339° = 156°34'12″ = 0.4098930568 rad
∠ C' = γ' = 172.8943931291° = 172°53'38″ = 0.12440242958 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 = 2.3+1.8+0.56 = 4.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4.66 }{ 2 } = 2.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.33 * (2.33-2.3)(2.33-1.8)(2.33-0.56) } ; ; T = sqrt{ 0.07 } = 0.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.26 }{ 2.3 } = 0.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.26 }{ 1.8 } = 0.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.26 }{ 0.56 } = 0.91 ; ;

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{ 1.8**2+0.56**2-2.3**2 }{ 2 * 1.8 * 0.56 } ) = 149° 27'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.3**2+0.56**2-1.8**2 }{ 2 * 2.3 * 0.56 } ) = 23° 25'48" ; ; gamma = 180° - alpha - beta = 180° - 149° 27'50" - 23° 25'48" = 7° 6'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.26 }{ 2.33 } = 0.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.3 }{ 2 * sin 149° 27'50" } = 2.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.8**2+2 * 0.56**2 - 2.3**2 } }{ 2 } = 0.674 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.56**2+2 * 2.3**2 - 1.8**2 } }{ 2 } = 1.411 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.8**2+2 * 2.3**2 - 0.56**2 } }{ 2 } = 2.046 ; ;
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