Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 64   b = 66   c = 116.4077283213

Area: T = 1683.97662325
Perimeter: p = 246.4077283213
Semiperimeter: s = 123.2043641606

Angle ∠ A = α = 265.9999937386° = 26° = 0.45437854962 rad
Angle ∠ B = β = 26.877658° = 26°52'36″ = 0.46990848127 rad
Angle ∠ C = γ = 127.1233426261° = 127°7'24″ = 2.21987223447 rad

Height: ha = 52.62442572655
Height: hb = 51.03295828029
Height: hc = 28.93224892055

Median: ma = 89.04767730605
Median: mb = 87.94550271049
Median: mc = 28.95440343261

Inradius: r = 13.66882342384
Circumradius: R = 72.99875214024

Vertex coordinates: A[116.4077283213; 0] B[0; 0] C[57.08768729953; 28.93224892055]
Centroid: CG[57.83113854027; 9.64441630685]
Coordinates of the circumscribed circle: U[58.20436416064; -44.05664891321]
Coordinates of the inscribed circle: I[57.20436416064; 13.66882342384]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1544.000006261° = 154° = 0.45437854962 rad
∠ B' = β' = 153.123342° = 153°7'24″ = 0.46990848127 rad
∠ C' = γ' = 52.87765737386° = 52°52'36″ = 2.21987223447 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 64 ; ; b = 66 ; ; beta = 26° 52'36" ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 66**2 = 64**2 + c**2 -2 * 66 * c * cos (26° 52'36") ; ; ; ; c**2 -114.174c -260 =0 ; ; p=1; q=-114.173745991; r=-260 ; ; D = q**2 - 4pr = 114.174**2 - 4 * 1 * (-260) = 14075.6442735 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 114.17 ± sqrt{ 14075.64 } }{ 2 } ; ; c_{1,2} = 57.0868729953 ± 59.3204102175 ; ;
c_{1} = 116.407283213 ; ; c_{2} = -2.23353722228 ; ; ; ; (c -116.407283213) (c +2.23353722228) = 0 ; ; ; ; c>0 ; ;


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 = 64 ; ; b = 66 ; ; c = 116.41 ; ;

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

p = a+b+c = 64+66+116.41 = 246.41 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 246.41 }{ 2 } = 123.2 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 123.2 * (123.2-64)(123.2-66)(123.2-116.41) } ; ; T = sqrt{ 2835775.95 } = 1683.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1683.98 }{ 64 } = 52.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1683.98 }{ 66 } = 51.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1683.98 }{ 116.41 } = 28.93 ; ;

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{ 64**2-66**2-116.41**2 }{ 2 * 66 * 116.41 } ) = 26° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 66**2-64**2-116.41**2 }{ 2 * 64 * 116.41 } ) = 26° 52'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 116.41**2-64**2-66**2 }{ 2 * 66 * 64 } ) = 127° 7'24" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1683.98 }{ 123.2 } = 13.67 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 64 }{ 2 * sin 26° } = 73 ; ;




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