Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 135   b = 90   c = 191.96

Area: T = 5475.759889418
Perimeter: p = 416.96
Semiperimeter: s = 208.48

Angle ∠ A = α = 39.33884807562° = 39°20'19″ = 0.68765860119 rad
Angle ∠ B = β = 24.99988646155° = 24°59'56″ = 0.43663124968 rad
Angle ∠ C = γ = 115.6632654628° = 115°39'46″ = 2.01986941449 rad

Height: ha = 81.12223539878
Height: hb = 121.6843530982
Height: hc = 57.05110407812

Median: ma = 133.8588398317
Median: mb = 159.7244202299
Median: mc = 62.85217271044

Inradius: r = 26.2655152025
Circumradius: R = 106.4843596387

Vertex coordinates: A[191.96; 0] B[0; 0] C[122.3532681809; 57.05110407812]
Centroid: CG[104.7710893936; 19.01770135937]
Coordinates of the circumscribed circle: U[95.98; -46.11550289982]
Coordinates of the inscribed circle: I[118.48; 26.2655152025]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.6621519244° = 140°39'41″ = 0.68765860119 rad
∠ B' = β' = 155.0011135385° = 155°4″ = 0.43663124968 rad
∠ C' = γ' = 64.33773453717° = 64°20'14″ = 2.01986941449 rad

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How did we calculate this triangle?

a = 135 ; ; b = 90 ; ; c = 191.96 ; ;

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

p = a+b+c = 135+90+191.96 = 416.96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 416.96 }{ 2 } = 208.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 208.48 * (208.48-135)(208.48-90)(208.48-191.96) } ; ; T = sqrt{ 29983935.47 } = 5475.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5475.76 }{ 135 } = 81.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5475.76 }{ 90 } = 121.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5475.76 }{ 191.96 } = 57.05 ; ;

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{ 90**2+191.96**2-135**2 }{ 2 * 90 * 191.96 } ) = 39° 20'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 135**2+191.96**2-90**2 }{ 2 * 135 * 191.96 } ) = 24° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 39° 20'19" - 24° 59'56" = 115° 39'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5475.76 }{ 208.48 } = 26.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 135 }{ 2 * sin 39° 20'19" } = 106.48 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 191.96**2 - 135**2 } }{ 2 } = 133.858 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 191.96**2+2 * 135**2 - 90**2 } }{ 2 } = 159.724 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 135**2 - 191.96**2 } }{ 2 } = 62.852 ; ;
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