Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 9.201   b = 102.087   c = 100.7329891334

Area: T = 460.9521902755
Perimeter: p = 212.0187891334
Semiperimeter: s = 106.0098945667

Angle ∠ A = α = 5.14435494443° = 5°8'37″ = 0.0989771873 rad
Angle ∠ B = β = 95.90114505557° = 95°54'5″ = 1.67437960696 rad
Angle ∠ C = γ = 78.955° = 78°57'18″ = 1.37880247109 rad

Height: ha = 100.1966044507
Height: hb = 9.0310570058
Height: hc = 9.15222366727

Median: ma = 101.3066311197
Median: mb = 50.10113553945
Median: mc = 52.12108138169

Inradius: r = 4.34882358951
Circumradius: R = 51.31554609408

Vertex coordinates: A[100.7329891334; 0] B[0; 0] C[-0.94660258382; 9.15222366727]
Centroid: CG[33.26112884987; 3.05107455576]
Coordinates of the circumscribed circle: U[50.36549456672; 9.83110111133]
Coordinates of the inscribed circle: I[3.92219456672; 4.34882358951]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.8566450556° = 174°51'23″ = 0.0989771873 rad
∠ B' = β' = 84.09985494443° = 84°5'55″ = 1.67437960696 rad
∠ C' = γ' = 101.045° = 101°2'42″ = 1.37880247109 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 = 9.2 ; ; b = 102.09 ; ; gamma = 78° 57'18" ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 9.2**2+102.09**2 - 2 * 9.2 * 102.09 * cos(78° 57'18") } ; ; c = 100.73 ; ;


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 = 9.2 ; ; b = 102.09 ; ; c = 100.73 ; ;

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

p = a+b+c = 9.2+102.09+100.73 = 212.02 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 212.02 }{ 2 } = 106.01 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 106.01 * (106.01-9.2)(106.01-102.09)(106.01-100.73) } ; ; T = sqrt{ 212476.66 } = 460.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 460.95 }{ 9.2 } = 100.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 460.95 }{ 102.09 } = 9.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 460.95 }{ 100.73 } = 9.15 ; ;

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{ 9.2**2-102.09**2-100.73**2 }{ 2 * 102.09 * 100.73 } ) = 5° 8'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 102.09**2-9.2**2-100.73**2 }{ 2 * 9.2 * 100.73 } ) = 95° 54'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 100.73**2-9.2**2-102.09**2 }{ 2 * 102.09 * 9.2 } ) = 78° 57'18" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 460.95 }{ 106.01 } = 4.35 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.2 }{ 2 * sin 5° 8'37" } = 51.32 ; ;




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