Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 10000   b = 2000   c = 10198.03990272

Area: T = 10000000
Perimeter: p = 22198.03990272
Semiperimeter: s = 11099.02195136

Angle ∠ A = α = 78.6990067526° = 78°41'24″ = 1.37334007669 rad
Angle ∠ B = β = 11.3109932474° = 11°18'36″ = 0.19773955598 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 2000
Height: hb = 10000
Height: hc = 1961.161135138

Median: ma = 5385.165480713
Median: mb = 10049.87656211
Median: mc = 5099.021951359

Inradius: r = 900.9880486407
Circumradius: R = 5099.021951359

Vertex coordinates: A[10198.03990272; 0] B[0; 0] C[9805.807675691; 1961.161135138]
Centroid: CG[6667.94985947; 653.7220450461]
Coordinates of the circumscribed circle: U[5099.021951359; -0]
Coordinates of the inscribed circle: I[9099.021951359; 900.9880486407]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.3109932474° = 101°18'36″ = 1.37334007669 rad
∠ B' = β' = 168.6990067526° = 168°41'24″ = 0.19773955598 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 = 10000 ; ; b = 2000 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 10000**2+2000**2 - 2 * 10000 * 2000 * cos(90° ) } ; ; c = 10198.04 ; ;


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 = 10000 ; ; b = 2000 ; ; c = 10198.04 ; ;

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

p = a+b+c = 10000+2000+10198.04 = 22198.04 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22198.04 }{ 2 } = 11099.02 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11099.02 * (11099.02-10000)(11099.02-2000)(11099.02-10198.04) } ; ; T = sqrt{ 1 * 10**{ 14 } } = 10000000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10000000 }{ 10000 } = 2000 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10000000 }{ 2000 } = 10000 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10000000 }{ 10198.04 } = 1961.16 ; ;

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{ 10000**2-2000**2-10198.04**2 }{ 2 * 2000 * 10198.04 } ) = 78° 41'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2000**2-10000**2-10198.04**2 }{ 2 * 10000 * 10198.04 } ) = 11° 18'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10198.04**2-10000**2-2000**2 }{ 2 * 2000 * 10000 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10000000 }{ 11099.02 } = 900.98 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10000 }{ 2 * sin 78° 41'24" } = 5099.02 ; ;




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