Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 50   b = 80   c = 94.34398113206

Area: T = 2000
Perimeter: p = 224.3439811321
Semiperimeter: s = 112.176990566

Angle ∠ A = α = 32.00553832081° = 32°19″ = 0.55985993153 rad
Angle ∠ B = β = 57.99546167919° = 57°59'41″ = 1.01221970115 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 80
Height: hb = 50
Height: hc = 42.43999152003

Median: ma = 83.81552730712
Median: mb = 64.03112423743
Median: mc = 47.17699056603

Inradius: r = 17.83300943397
Circumradius: R = 47.17699056603

Vertex coordinates: A[94.34398113206; 0] B[0; 0] C[26.54999470002; 42.43999152003]
Centroid: CG[40.28799194402; 14.13333050668]
Coordinates of the circumscribed circle: U[47.17699056603; 0]
Coordinates of the inscribed circle: I[32.17699056603; 17.83300943397]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.9954616792° = 147°59'41″ = 0.55985993153 rad
∠ B' = β' = 122.0055383208° = 122°19″ = 1.01221970115 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 = 50 ; ; b = 80 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 50**2+80**2 - 2 * 50 * 80 * cos(90° ) } ; ; c = 94.34 ; ;


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 = 50 ; ; b = 80 ; ; c = 94.34 ; ;

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

p = a+b+c = 50+80+94.34 = 224.34 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 224.34 }{ 2 } = 112.17 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 112.17 * (112.17-50)(112.17-80)(112.17-94.34) } ; ; T = sqrt{ 4000000 } = 2000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2000 }{ 50 } = 80 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2000 }{ 80 } = 50 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2000 }{ 94.34 } = 42.4 ; ;

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{ 50**2-80**2-94.34**2 }{ 2 * 80 * 94.34 } ) = 32° 19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 80**2-50**2-94.34**2 }{ 2 * 50 * 94.34 } ) = 57° 59'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 94.34**2-50**2-80**2 }{ 2 * 80 * 50 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2000 }{ 112.17 } = 17.83 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 32° 19" } = 47.17 ; ;




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