Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 100   b = 40   c = 91.65

Area: T = 18332.99999869
Perimeter: p = 231.65
Semiperimeter: s = 115.825

Angle ∠ A = α = 90.00221685187° = 90°8″ = 1.57108341746 rad
Angle ∠ B = β = 23.57881784603° = 23°34'41″ = 0.41215168458 rad
Angle ∠ C = γ = 66.4219653021° = 66°25'11″ = 1.15992416332 rad

Height: ha = 36.66599999737
Height: hb = 91.65499999344
Height: hc = 409.9999999714

Median: ma = 49.99986124807
Median: mb = 93.80875756536
Median: mc = 60.82881955593

Inradius: r = 15.82655989526
Circumradius: R = 500.0000000358

Vertex coordinates: A[91.65; 0] B[0; 0] C[91.65215139116; 409.9999999714]
Centroid: CG[61.10105046372; 13.33333333238]
Coordinates of the circumscribed circle: U[45.825; 20.00217343893]
Coordinates of the inscribed circle: I[75.825; 15.82655989526]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99878314813° = 89°59'52″ = 1.57108341746 rad
∠ B' = β' = 156.422182154° = 156°25'19″ = 0.41215168458 rad
∠ C' = γ' = 113.5880346979° = 113°34'49″ = 1.15992416332 rad

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How did we calculate this triangle?

a = 100 ; ; b = 40 ; ; c = 91.65 ; ;

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

p = a+b+c = 100+40+91.65 = 231.65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 231.65 }{ 2 } = 115.83 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 115.83 * (115.83-100)(115.83-40)(115.83-91.65) } ; ; T = sqrt{ 3359889 } = 1833 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1833 }{ 100 } = 36.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1833 }{ 40 } = 91.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1833 }{ 91.65 } = 40 ; ;

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{ 40**2+91.65**2-100**2 }{ 2 * 40 * 91.65 } ) = 90° 8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+91.65**2-40**2 }{ 2 * 100 * 91.65 } ) = 23° 34'41" ; ; gamma = 180° - alpha - beta = 180° - 90° 8" - 23° 34'41" = 66° 25'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1833 }{ 115.83 } = 15.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 90° 8" } = 50 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 91.65**2 - 100**2 } }{ 2 } = 49.999 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 91.65**2+2 * 100**2 - 40**2 } }{ 2 } = 93.808 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 100**2 - 91.65**2 } }{ 2 } = 60.828 ; ;
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