Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Obtuse scalene triangle.

Sides: a = 4.3   b = 2.5   c = 3.30545523739

Area: T = 4.11774888818
Perimeter: p = 10.10545523739
Semiperimeter: s = 5.05222761869

Angle ∠ A = α = 94.58220000115° = 94°34'55″ = 1.65107673133 rad
Angle ∠ B = β = 35.41879999885° = 35°25'5″ = 0.61881607143 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 1.91551111078
Height: hb = 3.29439911054
Height: hc = 2.49220100612

Median: ma = 1.99106112619
Median: mb = 3.62552631899
Median: mc = 3.10548322663

Inradius: r = 0.81549769984
Circumradius: R = 2.15768933784

Vertex coordinates: A[3.30545523739; 0] B[0; 0] C[3.5044266807; 2.49220100612]
Centroid: CG[2.27696063936; 0.83106700204]
Coordinates of the circumscribed circle: U[1.65222761869; 1.38664243391]
Coordinates of the inscribed circle: I[2.55222761869; 0.81549769984]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 85.41879999885° = 85°25'5″ = 1.65107673133 rad
∠ B' = β' = 144.5822000011° = 144°34'55″ = 0.61881607143 rad
∠ C' = γ' = 130° = 0.8732664626 rad

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How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 4.3 ; ; b = 2.5 ; ; gamma = 50° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 4.3**2+2.5**2 - 2 * 4.3 * 2.5 * cos(50° ) } ; ; c = 3.3 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 4.3 ; ; b = 2.5 ; ; c = 3.3 ; ;

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

p = a+b+c = 4.3+2.5+3.3 = 10.1 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.1 }{ 2 } = 5.05 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.05 * (5.05-4.3)(5.05-2.5)(5.05-3.3) } ; ; T = sqrt{ 16.95 } = 4.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.12 }{ 4.3 } = 1.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.12 }{ 2.5 } = 3.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.12 }{ 3.3 } = 2.49 ; ;

6. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 4.3**2-2.5**2-3.3**2 }{ 2 * 2.5 * 3.3 } ) = 94° 34'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-4.3**2-3.3**2 }{ 2 * 4.3 * 3.3 } ) = 35° 25'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.3**2-4.3**2-2.5**2 }{ 2 * 2.5 * 4.3 } ) = 50° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.12 }{ 5.05 } = 0.81 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.3 }{ 2 * sin 94° 34'55" } = 2.16 ; ;




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