Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 40   b = 44.42   c = 59.78

Area: T = 888.4399990779
Perimeter: p = 144.2
Semiperimeter: s = 72.1

Angle ∠ A = α = 41.99991899834° = 41°59'57″ = 0.73330241484 rad
Angle ∠ B = β = 47.9932554884° = 47°59'33″ = 0.83876280992 rad
Angle ∠ C = γ = 90.00882551326° = 90°30″ = 1.5710940406 rad

Height: ha = 44.42199995389
Height: hb = 409.9999995848
Height: hc = 29.72223148471

Median: ma = 48.7177475304
Median: mb = 45.75552193744
Median: mc = 29.88657173245

Inradius: r = 12.32217751842
Circumradius: R = 29.89900003102

Vertex coordinates: A[59.78; 0] B[0; 0] C[26.76990866511; 29.72223148471]
Centroid: CG[28.85496955504; 9.90774382824]
Coordinates of the circumscribed circle: U[29.89; -0.00443065286]
Coordinates of the inscribed circle: I[27.68; 12.32217751842]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0010810017° = 138°3″ = 0.73330241484 rad
∠ B' = β' = 132.0077445116° = 132°27″ = 0.83876280992 rad
∠ C' = γ' = 89.99217448674° = 89°59'30″ = 1.5710940406 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 = 40+44.42+59.78 = 144.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144.2 }{ 2 } = 72.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.1 * (72.1-40)(72.1-44.42)(72.1-59.78) } ; ; T = sqrt{ 789254.54 } = 888.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 888.4 }{ 40 } = 44.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 888.4 }{ 44.42 } = 40 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 888.4 }{ 59.78 } = 29.72 ; ;

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{ 44.42**2+59.78**2-40**2 }{ 2 * 44.42 * 59.78 } ) = 41° 59'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 40**2+59.78**2-44.42**2 }{ 2 * 40 * 59.78 } ) = 47° 59'33" ; ;
 gamma = 180° - alpha - beta = 180° - 41° 59'57" - 47° 59'33" = 90° 30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 888.4 }{ 72.1 } = 12.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 40 }{ 2 * sin 41° 59'57" } = 29.89 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.42**2+2 * 59.78**2 - 40**2 } }{ 2 } = 48.717 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 59.78**2+2 * 40**2 - 44.42**2 } }{ 2 } = 45.755 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.42**2+2 * 40**2 - 59.78**2 } }{ 2 } = 29.886 ; ;
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