Triangle calculator SAS

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


Acute scalene triangle.

Sides: a = 70   b = 50   c = 62.4549979984

Area: T = 1515.544445662
Perimeter: p = 182.4549979984
Semiperimeter: s = 91.2254989992

Angle ∠ A = α = 76.1022113752° = 76°6'8″ = 1.32882324527 rad
Angle ∠ B = β = 43.8987886248° = 43°53'52″ = 0.76661626497 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 43.30112701892
Height: hb = 60.62217782649
Height: hc = 48.53662671697

Median: ma = 44.44109720866
Median: mb = 61.44110286372
Median: mc = 52.20215325446

Inradius: r = 16.61332597741
Circumradius: R = 36.05655127546

Vertex coordinates: A[62.4549979984; 0] B[0; 0] C[50.44403684486; 48.53662671697]
Centroid: CG[37.63301161442; 16.17987557232]
Coordinates of the circumscribed circle: U[31.2254989992; 18.02877563773]
Coordinates of the inscribed circle: I[41.2254989992; 16.61332597741]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.8987886248° = 103°53'52″ = 1.32882324527 rad
∠ B' = β' = 136.1022113752° = 136°6'8″ = 0.76661626497 rad
∠ C' = γ' = 120° = 1.04771975512 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 = 70 ; ; b = 50 ; ; gamma = 60° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 70**2+50**2 - 2 * 70 * 50 * cos(60° ) } ; ; c = 62.45 ; ;


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 = 70 ; ; b = 50 ; ; c = 62.45 ; ;

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

p = a+b+c = 70+50+62.45 = 182.45 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 182.45 }{ 2 } = 91.22 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 91.22 * (91.22-70)(91.22-50)(91.22-62.45) } ; ; T = sqrt{ 2296875 } = 1515.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1515.54 }{ 70 } = 43.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1515.54 }{ 50 } = 60.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1515.54 }{ 62.45 } = 48.54 ; ;

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{ 70**2-50**2-62.45**2 }{ 2 * 50 * 62.45 } ) = 76° 6'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50**2-70**2-62.45**2 }{ 2 * 70 * 62.45 } ) = 43° 53'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62.45**2-70**2-50**2 }{ 2 * 50 * 70 } ) = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1515.54 }{ 91.22 } = 16.61 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 70 }{ 2 * sin 76° 6'8" } = 36.06 ; ;




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