Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 3.516   b = 356   c = 354.6987864537

Area: T = 580.2766161013
Perimeter: p = 714.2143864537
Semiperimeter: s = 357.1076932268

Angle ∠ A = α = 0.5276604905° = 0°31'36″ = 0.00991909894 rad
Angle ∠ B = β = 111.4733395095° = 111°28'24″ = 1.94655777728 rad
Angle ∠ C = γ = 68° = 1.18768238914 rad

Height: ha = 330.0777452226
Height: hb = 3.26599784327
Height: hc = 3.27219461775

Median: ma = 355.3455180057
Median: mb = 176.7132955613
Median: mc = 178.666599383

Inradius: r = 1.62549367026
Circumradius: R = 191.2776985028

Vertex coordinates: A[354.6987864537; 0] B[0; 0] C[-1.28770991461; 3.27219461775]
Centroid: CG[117.8043588464; 1.09106487258]
Coordinates of the circumscribed circle: U[177.3498932268; 71.65436197603]
Coordinates of the inscribed circle: I[1.10769322684; 1.62549367026]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.4733395095° = 179°28'24″ = 0.00991909894 rad
∠ B' = β' = 68.5276604905° = 68°31'36″ = 1.94655777728 rad
∠ C' = γ' = 112° = 1.18768238914 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 = 3.52 ; ; b = 356 ; ; gamma = 68° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 3.52**2+356**2 - 2 * 3.52 * 356 * cos(68° ) } ; ; c = 354.7 ; ;


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 = 3.52 ; ; b = 356 ; ; c = 354.7 ; ;

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

p = a+b+c = 3.52+356+354.7 = 714.21 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 714.21 }{ 2 } = 357.11 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 357.11 * (357.11-3.52)(357.11-356)(357.11-354.7) } ; ; T = sqrt{ 336720.42 } = 580.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 580.28 }{ 3.52 } = 330.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 580.28 }{ 356 } = 3.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 580.28 }{ 354.7 } = 3.27 ; ;

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{ 3.52**2-356**2-354.7**2 }{ 2 * 356 * 354.7 } ) = 0° 31'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 356**2-3.52**2-354.7**2 }{ 2 * 3.52 * 354.7 } ) = 111° 28'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 354.7**2-3.52**2-356**2 }{ 2 * 356 * 3.52 } ) = 68° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 580.28 }{ 357.11 } = 1.62 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.52 }{ 2 * sin 0° 31'36" } = 191.28 ; ;




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