Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 60.5   b = 216   c = 169.2598748677

Area: T = 3653.766643128
Perimeter: p = 445.7598748677
Semiperimeter: s = 222.8799374339

Angle ∠ A = α = 11.53298492514° = 11°31'47″ = 0.20112338317 rad
Angle ∠ B = β = 134.4770150749° = 134°28'13″ = 2.34769468762 rad
Angle ∠ C = γ = 34° = 0.59334119457 rad

Height: ha = 120.786566715
Height: hb = 33.831117066
Height: hc = 43.17437379585

Median: ma = 191.6769505926
Median: mb = 67.01103499607
Median: mc = 134.1499148335

Inradius: r = 16.39334704237
Circumradius: R = 151.3422003472

Vertex coordinates: A[169.2598748677; 0] B[0; 0] C[-42.3832524119; 43.17437379585]
Centroid: CG[42.29220748527; 14.39112459862]
Coordinates of the circumscribed circle: U[84.62993743385; 125.4688207184]
Coordinates of the inscribed circle: I[6.87993743385; 16.39334704237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.4770150749° = 168°28'13″ = 0.20112338317 rad
∠ B' = β' = 45.53298492514° = 45°31'47″ = 2.34769468762 rad
∠ C' = γ' = 146° = 0.59334119457 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 = 60.5 ; ; b = 216 ; ; gamma = 34° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 60.5**2+216**2 - 2 * 60.5 * 216 * cos(34° ) } ; ; c = 169.26 ; ;


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 = 60.5 ; ; b = 216 ; ; c = 169.26 ; ;

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

p = a+b+c = 60.5+216+169.26 = 445.76 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 445.76 }{ 2 } = 222.88 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 222.88 * (222.88-60.5)(222.88-216)(222.88-169.26) } ; ; T = sqrt{ 13350009.13 } = 3653.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3653.77 }{ 60.5 } = 120.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3653.77 }{ 216 } = 33.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3653.77 }{ 169.26 } = 43.17 ; ;

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{ 60.5**2-216**2-169.26**2 }{ 2 * 216 * 169.26 } ) = 11° 31'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 216**2-60.5**2-169.26**2 }{ 2 * 60.5 * 169.26 } ) = 134° 28'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 169.26**2-60.5**2-216**2 }{ 2 * 216 * 60.5 } ) = 34° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3653.77 }{ 222.88 } = 16.39 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 60.5 }{ 2 * sin 11° 31'47" } = 151.34 ; ;




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