Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 42   b = 35   c = 66.77657440992

Area: T = 636.5298671782
Perimeter: p = 143.7765744099
Semiperimeter: s = 71.88878720496

Angle ∠ A = α = 33.00444915989° = 33°16″ = 0.57660370463 rad
Angle ∠ B = β = 26.99655084011° = 26°59'44″ = 0.47111605048 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 30.31108891325
Height: hb = 36.37330669589
Height: hc = 19.06546672791

Median: ma = 49
Median: mb = 52.96546108265
Median: mc = 19.48771752699

Inradius: r = 8.85444653449
Circumradius: R = 38.5532993831

Vertex coordinates: A[66.77657440992; 0] B[0; 0] C[37.4243768671; 19.06546672791]
Centroid: CG[34.73331709234; 6.3554889093]
Coordinates of the circumscribed circle: U[33.38878720496; -19.27664969155]
Coordinates of the inscribed circle: I[36.88878720496; 8.85444653449]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9965508401° = 146°59'44″ = 0.57660370463 rad
∠ B' = β' = 153.0044491599° = 153°16″ = 0.47111605048 rad
∠ C' = γ' = 60° = 2.09443951024 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 42 ; ; b = 35 ; ; gamma = 120° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 42**2+35**2 - 2 * 42 * 35 * cos 120° } ; ; c = 66.78 ; ;
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 = 42 ; ; b = 35 ; ; c = 66.78 ; ;

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

p = a+b+c = 42+35+66.78 = 143.78 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 143.78 }{ 2 } = 71.89 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 71.89 * (71.89-42)(71.89-35)(71.89-66.78) } ; ; T = sqrt{ 405168.75 } = 636.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 636.53 }{ 42 } = 30.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 636.53 }{ 35 } = 36.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 636.53 }{ 66.78 } = 19.06 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 35**2+66.78**2-42**2 }{ 2 * 35 * 66.78 } ) = 33° 16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 42**2+66.78**2-35**2 }{ 2 * 42 * 66.78 } ) = 26° 59'44" ; ; gamma = 180° - alpha - beta = 180° - 33° 16" - 26° 59'44" = 120° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 636.53 }{ 71.89 } = 8.85 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 42 }{ 2 * sin 33° 16" } = 38.55 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 66.78**2 - 42**2 } }{ 2 } = 49 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.78**2+2 * 42**2 - 35**2 } }{ 2 } = 52.965 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 42**2 - 66.78**2 } }{ 2 } = 19.487 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.