Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 50   b = 40   c = 11.35

Area: T = 119.8330417542
Perimeter: p = 101.35
Semiperimeter: s = 50.675

Angle ∠ A = α = 148.1377180839° = 148°8'14″ = 2.58554815503 rad
Angle ∠ B = β = 24.98105035624° = 24°58'50″ = 0.4365992036 rad
Angle ∠ C = γ = 6.88223155987° = 6°52'56″ = 0.12201190674 rad

Height: ha = 4.79332167017
Height: hb = 5.99215208771
Height: hc = 21.11554920779

Median: ma = 15.47329198925
Median: mb = 30.23992336212
Median: mc = 44.92198661507

Inradius: r = 2.3654685102
Circumradius: R = 47.35985932219

Vertex coordinates: A[11.35; 0] B[0; 0] C[45.32325770925; 21.11554920779]
Centroid: CG[18.89108590308; 7.03884973593]
Coordinates of the circumscribed circle: U[5.675; 47.01773449587]
Coordinates of the inscribed circle: I[10.675; 2.3654685102]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 31.86328191611° = 31°51'46″ = 2.58554815503 rad
∠ B' = β' = 155.0199496438° = 155°1'10″ = 0.4365992036 rad
∠ C' = γ' = 173.1187684401° = 173°7'4″ = 0.12201190674 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 = 50+40+11.35 = 101.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 101.35 }{ 2 } = 50.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.68 * (50.68-50)(50.68-40)(50.68-11.35) } ; ; T = sqrt{ 14359.33 } = 119.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.83 }{ 50 } = 4.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.83 }{ 40 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.83 }{ 11.35 } = 21.12 ; ;

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+11.35**2-50**2 }{ 2 * 40 * 11.35 } ) = 148° 8'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+11.35**2-40**2 }{ 2 * 50 * 11.35 } ) = 24° 58'50" ; ; gamma = 180° - alpha - beta = 180° - 148° 8'14" - 24° 58'50" = 6° 52'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.83 }{ 50.68 } = 2.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 50 }{ 2 * sin 148° 8'14" } = 47.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 11.35**2 - 50**2 } }{ 2 } = 15.473 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.35**2+2 * 50**2 - 40**2 } }{ 2 } = 30.239 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 50**2 - 11.35**2 } }{ 2 } = 44.92 ; ;
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