Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 1070   b = 2445   c = 2668.881085159

Area: T = 1308075
Perimeter: p = 6183.881085159
Semiperimeter: s = 3091.94404258

Angle ∠ A = α = 23.63655240275° = 23°38'8″ = 0.41325177147 rad
Angle ∠ B = β = 66.36444759725° = 66°21'52″ = 1.15882786121 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 2445
Height: hb = 1070
Height: hc = 980.2422335823

Median: ma = 2502.848837735
Median: mb = 1624.625495672
Median: mc = 1334.44404258

Inradius: r = 423.0659574204
Circumradius: R = 1334.44404258

Vertex coordinates: A[2668.881085159; 0] B[0; 0] C[428.981130852; 980.2422335823]
Centroid: CG[1032.621072004; 326.7477445275]
Coordinates of the circumscribed circle: U[1334.44404258; -0]
Coordinates of the inscribed circle: I[646.9440425796; 423.0659574204]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.3644475972° = 156°21'52″ = 0.41325177147 rad
∠ B' = β' = 113.6365524028° = 113°38'8″ = 1.15882786121 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 = 1070 ; ; b = 2445 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 1070**2+2445**2 - 2 * 1070 * 2445 * cos(90° ) } ; ; c = 2668.88 ; ;


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 = 1070 ; ; b = 2445 ; ; c = 2668.88 ; ;

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

p = a+b+c = 1070+2445+2668.88 = 6183.88 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6183.88 }{ 2 } = 3091.94 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3091.94 * (3091.94-1070)(3091.94-2445)(3091.94-2668.88) } ; ; T = sqrt{ 1.711 * 10**{ 12 } } = 1308075 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1308075 }{ 1070 } = 2445 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1308075 }{ 2445 } = 1070 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1308075 }{ 2668.88 } = 980.24 ; ;

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{ 1070**2-2445**2-2668.88**2 }{ 2 * 2445 * 2668.88 } ) = 23° 38'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2445**2-1070**2-2668.88**2 }{ 2 * 1070 * 2668.88 } ) = 66° 21'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2668.88**2-1070**2-2445**2 }{ 2 * 2445 * 1070 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1308075 }{ 3091.94 } = 423.06 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1070 }{ 2 * sin 23° 38'8" } = 1334.44 ; ;




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