Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 8.14   b = 33   c = 33.98991100207

Area: T = 134.31
Perimeter: p = 75.12991100207
Semiperimeter: s = 37.56545550104

Angle ∠ A = α = 13.85663515017° = 13°51'23″ = 0.2421838956 rad
Angle ∠ B = β = 76.14436484983° = 76°8'37″ = 1.32989573708 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 33
Height: hb = 8.14
Height: hc = 7.90331195532

Median: ma = 33.25500360902
Median: mb = 18.39986303838
Median: mc = 16.99545550104

Inradius: r = 3.57554449896
Circumradius: R = 16.99545550104

Vertex coordinates: A[33.98991100207; 0] B[0; 0] C[1.94994361565; 7.90331195532]
Centroid: CG[11.98795153924; 2.63443731844]
Coordinates of the circumscribed circle: U[16.99545550104; -0]
Coordinates of the inscribed circle: I[4.56545550104; 3.57554449896]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1443648498° = 166°8'37″ = 0.2421838956 rad
∠ B' = β' = 103.8566351502° = 103°51'23″ = 1.32989573708 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 8.14 ; ; b = 33 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 8.14**2+33**2 - 2 * 8.14 * 33 * cos(90° ) } ; ; c = 33.99 ; ;


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 = 8.14 ; ; b = 33 ; ; c = 33.99 ; ;

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

p = a+b+c = 8.14+33+33.99 = 75.13 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75.13 }{ 2 } = 37.56 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.56 * (37.56-8.14)(37.56-33)(37.56-33.99) } ; ; T = sqrt{ 18039.18 } = 134.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.31 }{ 8.14 } = 33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.31 }{ 33 } = 8.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.31 }{ 33.99 } = 7.9 ; ;

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{ 8.14**2-33**2-33.99**2 }{ 2 * 33 * 33.99 } ) = 13° 51'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33**2-8.14**2-33.99**2 }{ 2 * 8.14 * 33.99 } ) = 76° 8'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 33.99**2-8.14**2-33**2 }{ 2 * 33 * 8.14 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.31 }{ 37.56 } = 3.58 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.14 }{ 2 * sin 13° 51'23" } = 16.99 ; ;




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