Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 25.51

Area: T = 1104.655002694
Perimeter: p = 215.51
Semiperimeter: s = 107.755

Angle ∠ A = α = 105.7876818166° = 105°47'13″ = 1.84663282822 rad
Angle ∠ B = β = 60.00331108208° = 60°11″ = 1.04772518453 rad
Angle ∠ C = γ = 14.21100710131° = 14°12'36″ = 0.24880125261 rad

Height: ha = 22.09330005388
Height: hb = 24.54877783764
Height: hc = 86.6055254954

Median: ma = 43.30656584063
Median: mb = 57.44989342808
Median: mc = 94.2732530331

Inradius: r = 10.25114967003
Circumradius: R = 51.96598955328

Vertex coordinates: A[25.51; 0] B[0; 0] C[49.99552979224; 86.6055254954]
Centroid: CG[25.16884326408; 28.8688418318]
Coordinates of the circumscribed circle: U[12.755; 50.37700379072]
Coordinates of the inscribed circle: I[17.755; 10.25114967003]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 74.21331818339° = 74°12'47″ = 1.84663282822 rad
∠ B' = β' = 119.9976889179° = 119°59'49″ = 1.04772518453 rad
∠ C' = γ' = 165.7989928987° = 165°47'24″ = 0.24880125261 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 = 100+90+25.51 = 215.51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 215.51 }{ 2 } = 107.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 107.76 * (107.76-100)(107.76-90)(107.76-25.51) } ; ; T = sqrt{ 1220251.68 } = 1104.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1104.65 }{ 100 } = 22.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1104.65 }{ 90 } = 24.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1104.65 }{ 25.51 } = 86.61 ; ;

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+25.51**2-100**2 }{ 2 * 90 * 25.51 } ) = 105° 47'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+25.51**2-90**2 }{ 2 * 100 * 25.51 } ) = 60° 11" ; ; gamma = 180° - alpha - beta = 180° - 105° 47'13" - 60° 11" = 14° 12'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1104.65 }{ 107.76 } = 10.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 105° 47'13" } = 51.96 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 25.51**2 - 100**2 } }{ 2 } = 43.306 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.51**2+2 * 100**2 - 90**2 } }{ 2 } = 57.449 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 100**2 - 25.51**2 } }{ 2 } = 94.273 ; ;
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