Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 263.93   b = 184.463263   c = 80.68804890408

Area: T = 1536.966550305
Perimeter: p = 529.0733119041
Semiperimeter: s = 264.537655952

Angle ∠ A = α = 168.0879973218° = 168°4'48″ = 2.93435489393 rad
Angle ∠ B = β = 8.33000267824° = 8°18' = 0.14548627954 rad
Angle ∠ C = γ = 3.62° = 3°37'12″ = 0.06331809189 rad

Height: ha = 11.64767662111
Height: hb = 16.66442479623
Height: hc = 38.11000542095

Median: ma = 53.41547953679
Median: mb = 171.9811329334
Median: mc = 224.0887969457

Inradius: r = 5.81100305902
Circumradius: R = 638.9132764641

Vertex coordinates: A[80.68804890408; 0] B[0; 0] C[261.1665523699; 38.11000542095]
Centroid: CG[113.9498670913; 12.77000180698]
Coordinates of the circumscribed circle: U[40.34402445204; 637.6387973691]
Coordinates of the inscribed circle: I[80.07439295204; 5.81100305902]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 11.92200267824° = 11°55'12″ = 2.93435489393 rad
∠ B' = β' = 171.7699973218° = 171°42' = 0.14548627954 rad
∠ C' = γ' = 176.38° = 176°22'48″ = 0.06331809189 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 = 263.93 ; ; b = 184.46 ; ; gamma = 3° 37'12" ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 263.93**2+184.46**2 - 2 * 263.93 * 184.46 * cos(3° 37'12") } ; ; c = 80.68 ; ;


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 = 263.93 ; ; b = 184.46 ; ; c = 80.68 ; ;

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

p = a+b+c = 263.93+184.46+80.68 = 529.07 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 529.07 }{ 2 } = 264.54 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 264.54 * (264.54-263.93)(264.54-184.46)(264.54-80.68) } ; ; T = sqrt{ 2362262.96 } = 1536.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1536.97 }{ 263.93 } = 11.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1536.97 }{ 184.46 } = 16.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1536.97 }{ 80.68 } = 38.1 ; ;

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{ 263.93**2-184.46**2-80.68**2 }{ 2 * 184.46 * 80.68 } ) = 168° 4'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 184.46**2-263.93**2-80.68**2 }{ 2 * 263.93 * 80.68 } ) = 8° 18' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 80.68**2-263.93**2-184.46**2 }{ 2 * 184.46 * 263.93 } ) = 3° 37'12" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1536.97 }{ 264.54 } = 5.81 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 263.93 }{ 2 * sin 168° 4'48" } = 638.91 ; ;




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