Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 17.2   b = 7.1   c = 10.92111449597

Area: T = 22.54770286629
Perimeter: p = 35.22111449597
Semiperimeter: s = 17.61105724798

Angle ∠ A = α = 144.4439824004° = 144°26'23″ = 2.52109504999 rad
Angle ∠ B = β = 13.89901759964° = 13°53'25″ = 0.24224293048 rad
Angle ∠ C = γ = 21.67° = 21°40'12″ = 0.37882128489 rad

Height: ha = 2.62217475189
Height: hb = 6.35112756797
Height: hc = 4.12990594981

Median: ma = 3.29985911561
Median: mb = 13.96325643639
Median: mc = 11.97110963655

Inradius: r = 1.28803120789
Circumradius: R = 14.78878711916

Vertex coordinates: A[10.92111449597; 0] B[0; 0] C[16.69770317021; 4.12990594981]
Centroid: CG[9.20660588873; 1.3766353166]
Coordinates of the circumscribed circle: U[5.46105724798; 13.74327538205]
Coordinates of the inscribed circle: I[10.51105724798; 1.28803120789]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 35.56601759964° = 35°33'37″ = 2.52109504999 rad
∠ B' = β' = 166.1109824004° = 166°6'35″ = 0.24224293048 rad
∠ C' = γ' = 158.33° = 158°19'48″ = 0.37882128489 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 = 17.2 ; ; b = 7.1 ; ; gamma = 21° 40'12" ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 17.2**2+7.1**2 - 2 * 17.2 * 7.1 * cos(21° 40'12") } ; ; c = 10.92 ; ;


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 = 17.2 ; ; b = 7.1 ; ; c = 10.92 ; ;

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

p = a+b+c = 17.2+7.1+10.92 = 35.22 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.22 }{ 2 } = 17.61 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.61 * (17.61-17.2)(17.61-7.1)(17.61-10.92) } ; ; T = sqrt{ 508.37 } = 22.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.55 }{ 17.2 } = 2.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.55 }{ 7.1 } = 6.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.55 }{ 10.92 } = 4.13 ; ;

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{ 17.2**2-7.1**2-10.92**2 }{ 2 * 7.1 * 10.92 } ) = 144° 26'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.1**2-17.2**2-10.92**2 }{ 2 * 17.2 * 10.92 } ) = 13° 53'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.92**2-17.2**2-7.1**2 }{ 2 * 7.1 * 17.2 } ) = 21° 40'12" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.55 }{ 17.61 } = 1.28 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.2 }{ 2 * sin 144° 26'23" } = 14.79 ; ;




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