Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 227   b = 142   c = 333.7421612616

Area: T = 12700.36993159
Perimeter: p = 702.7421612616
Semiperimeter: s = 351.3710806308

Angle ∠ A = α = 32.41103180398° = 32°24'37″ = 0.56656667614 rad
Angle ∠ B = β = 19.59896819602° = 19°35'23″ = 0.34219044496 rad
Angle ∠ C = γ = 128° = 2.23440214426 rad

Height: ha = 111.8987527012
Height: hb = 178.8788441069
Height: hc = 76.10989947181

Median: ma = 229.9811481854
Median: mb = 276.4333051562
Median: mc = 89.44662632097

Inradius: r = 36.1455203551
Circumradius: R = 211.7622092768

Vertex coordinates: A[333.7421612616; 0] B[0; 0] C[213.8610751245; 76.10989947181]
Centroid: CG[182.5344121287; 25.3769664906]
Coordinates of the circumscribed circle: U[166.8710806308; -130.3743762452]
Coordinates of the inscribed circle: I[209.3710806308; 36.1455203551]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.598968196° = 147°35'23″ = 0.56656667614 rad
∠ B' = β' = 160.411031804° = 160°24'37″ = 0.34219044496 rad
∠ C' = γ' = 52° = 2.23440214426 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 = 227 ; ; b = 142 ; ; gamma = 128° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 227**2+142**2 - 2 * 227 * 142 * cos(128° ) } ; ; c = 333.74 ; ;


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 = 227 ; ; b = 142 ; ; c = 333.74 ; ;

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

p = a+b+c = 227+142+333.74 = 702.74 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 702.74 }{ 2 } = 351.37 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 351.37 * (351.37-227)(351.37-142)(351.37-333.74) } ; ; T = sqrt{ 161299380.76 } = 12700.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12700.37 }{ 227 } = 111.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12700.37 }{ 142 } = 178.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12700.37 }{ 333.74 } = 76.11 ; ;

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{ 227**2-142**2-333.74**2 }{ 2 * 142 * 333.74 } ) = 32° 24'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 142**2-227**2-333.74**2 }{ 2 * 227 * 333.74 } ) = 19° 35'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 333.74**2-227**2-142**2 }{ 2 * 142 * 227 } ) = 128° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12700.37 }{ 351.37 } = 36.15 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 227 }{ 2 * sin 32° 24'37" } = 211.76 ; ;




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