Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 13.1   b = 8.7   c = 6.94875134668

Area: T = 27.77546332492
Perimeter: p = 28.74875134668
Semiperimeter: s = 14.37437567334

Angle ∠ A = α = 113.215531894° = 113°12'55″ = 1.97659800792 rad
Angle ∠ B = β = 37.61546810604° = 37°36'53″ = 0.65765000316 rad
Angle ∠ C = γ = 29.17° = 29°10'12″ = 0.50991125428 rad

Height: ha = 4.24404020228
Height: hb = 6.38549731607
Height: hc = 7.99655608239

Median: ma = 4.36876620388
Median: mb = 9.5440255326
Median: mc = 10.56332861439

Inradius: r = 1.93223155223
Circumradius: R = 7.12770797953

Vertex coordinates: A[6.94875134668; 0] B[0; 0] C[10.37769459434; 7.99655608239]
Centroid: CG[5.77548198034; 2.66551869413]
Coordinates of the circumscribed circle: U[3.47437567334; 6.22332050075]
Coordinates of the inscribed circle: I[5.67437567334; 1.93223155223]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 66.78546810604° = 66°47'5″ = 1.97659800792 rad
∠ B' = β' = 142.385531894° = 142°23'7″ = 0.65765000316 rad
∠ C' = γ' = 150.83° = 150°49'48″ = 0.50991125428 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 = 13.1 ; ; b = 8.7 ; ; gamma = 29° 10'12" ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 13.1**2+8.7**2 - 2 * 13.1 * 8.7 * cos(29° 10'12") } ; ; c = 6.95 ; ;


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 = 13.1 ; ; b = 8.7 ; ; c = 6.95 ; ;

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

p = a+b+c = 13.1+8.7+6.95 = 28.75 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28.75 }{ 2 } = 14.37 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.37 * (14.37-13.1)(14.37-8.7)(14.37-6.95) } ; ; T = sqrt{ 771.43 } = 27.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.77 }{ 13.1 } = 4.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.77 }{ 8.7 } = 6.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.77 }{ 6.95 } = 8 ; ;

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{ 13.1**2-8.7**2-6.95**2 }{ 2 * 8.7 * 6.95 } ) = 113° 12'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.7**2-13.1**2-6.95**2 }{ 2 * 13.1 * 6.95 } ) = 37° 36'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.95**2-13.1**2-8.7**2 }{ 2 * 8.7 * 13.1 } ) = 29° 10'12" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.77 }{ 14.37 } = 1.93 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.1 }{ 2 * sin 113° 12'55" } = 7.13 ; ;




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