Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 0.5   b = 0.33333333333   c = 0.6254630311

Area: T = 0.08330162248
Perimeter: p = 1.45879636443
Semiperimeter: s = 0.72989818221

Angle ∠ A = α = 52.88551383234° = 52°53'7″ = 0.92330197891 rad
Angle ∠ B = β = 32.11548616766° = 32°6'53″ = 0.56105100751 rad
Angle ∠ C = γ = 95° = 1.65880627894 rad

Height: ha = 0.33220648994
Height: hb = 0.4988097349
Height: hc = 0.26658091463

Median: ma = 0.43437477011
Median: mb = 0.54106512137
Median: mc = 0.28881228891

Inradius: r = 0.11438796913
Circumradius: R = 0.31435081486

Vertex coordinates: A[0.6254630311; 0] B[0; 0] C[0.4233492028; 0.26658091463]
Centroid: CG[0.3499374113; 0.08986030488]
Coordinates of the circumscribed circle: U[0.31223151555; -0.02773240356]
Coordinates of the inscribed circle: I[0.39656484888; 0.11438796913]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.1154861677° = 127°6'53″ = 0.92330197891 rad
∠ B' = β' = 147.8855138323° = 147°53'7″ = 0.56105100751 rad
∠ C' = γ' = 85° = 1.65880627894 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 = 0.5 ; ; b = 0.33 ; ; gamma = 95° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 0.5**2+0.33**2 - 2 * 0.5 * 0.33 * cos(95° ) } ; ; c = 0.62 ; ;


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 = 0.5 ; ; b = 0.33 ; ; c = 0.62 ; ;

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

p = a+b+c = 0.5+0.33+0.62 = 1.46 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1.46 }{ 2 } = 0.73 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.73 * (0.73-0.5)(0.73-0.33)(0.73-0.62) } ; ; T = sqrt{ 0.01 } = 0.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.08 }{ 0.5 } = 0.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.08 }{ 0.33 } = 0.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.08 }{ 0.62 } = 0.27 ; ;

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{ 0.5**2-0.33**2-0.62**2 }{ 2 * 0.33 * 0.62 } ) = 52° 53'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.33**2-0.5**2-0.62**2 }{ 2 * 0.5 * 0.62 } ) = 32° 6'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.62**2-0.5**2-0.33**2 }{ 2 * 0.33 * 0.5 } ) = 95° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.08 }{ 0.73 } = 0.11 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.5 }{ 2 * sin 52° 53'7" } = 0.31 ; ;




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