Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 150   b = 100   c = 227.5660164112

Area: T = 5745.333332339
Perimeter: p = 477.5660164112
Semiperimeter: s = 238.7880082056

Angle ∠ A = α = 30.32880804475° = 30°19'41″ = 0.52993248596 rad
Angle ∠ B = β = 19.67219195525° = 19°40'19″ = 0.34333397664 rad
Angle ∠ C = γ = 130° = 2.26989280276 rad

Height: ha = 76.60444443119
Height: hb = 114.9076666468
Height: hc = 50.4955071014

Median: ma = 158.9555384134
Median: mb = 186.1233115559
Median: mc = 57.48112397861

Inradius: r = 24.06111916787
Circumradius: R = 148.5299348497

Vertex coordinates: A[227.5660164112; 0] B[0; 0] C[141.245534613; 50.4955071014]
Centroid: CG[122.9355170081; 16.8321690338]
Coordinates of the circumscribed circle: U[113.7880082056; -95.47328248884]
Coordinates of the inscribed circle: I[138.7880082056; 24.06111916787]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.6721919552° = 149°40'19″ = 0.52993248596 rad
∠ B' = β' = 160.3288080448° = 160°19'41″ = 0.34333397664 rad
∠ C' = γ' = 50° = 2.26989280276 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 = 150 ; ; b = 100 ; ; gamma = 130° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 150**2+100**2 - 2 * 150 * 100 * cos(130° ) } ; ; c = 227.56 ; ;


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 = 150 ; ; b = 100 ; ; c = 227.56 ; ;

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

p = a+b+c = 150+100+227.56 = 477.56 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 477.56 }{ 2 } = 238.78 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 238.78 * (238.78-150)(238.78-100)(238.78-227.56) } ; ; T = sqrt{ 33008855 } = 5745.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5745.33 }{ 150 } = 76.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5745.33 }{ 100 } = 114.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5745.33 }{ 227.56 } = 50.5 ; ;

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{ 150**2-100**2-227.56**2 }{ 2 * 100 * 227.56 } ) = 30° 19'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 100**2-150**2-227.56**2 }{ 2 * 150 * 227.56 } ) = 19° 40'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 227.56**2-150**2-100**2 }{ 2 * 100 * 150 } ) = 130° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5745.33 }{ 238.78 } = 24.06 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 150 }{ 2 * sin 30° 19'41" } = 148.53 ; ;




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