Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 8.3   b = 7.6   c = 7.78

Area: T = 26.86110773395
Perimeter: p = 23.68
Semiperimeter: s = 11.84

Angle ∠ A = α = 65.30990063869° = 65°18'32″ = 1.14398571927 rad
Angle ∠ B = β = 56.29992790971° = 56°17'57″ = 0.98326077867 rad
Angle ∠ C = γ = 58.3921714516° = 58°23'30″ = 1.01991276742 rad

Height: ha = 6.47325487565
Height: hb = 7.0698704563
Height: hc = 6.90551612698

Median: ma = 6.47546969041
Median: mb = 7.09900775736
Median: mc = 6.94221106301

Inradius: r = 2.26986720726
Circumradius: R = 4.56875978833

Vertex coordinates: A[7.78; 0] B[0; 0] C[4.60552956298; 6.90551612698]
Centroid: CG[4.12884318766; 2.30217204233]
Coordinates of the circumscribed circle: U[3.89; 2.39439194689]
Coordinates of the inscribed circle: I[4.24; 2.26986720726]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.6910993613° = 114°41'28″ = 1.14398571927 rad
∠ B' = β' = 123.7010720903° = 123°42'3″ = 0.98326077867 rad
∠ C' = γ' = 121.6088285484° = 121°36'30″ = 1.01991276742 rad

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How did we calculate this triangle?

a = 8.3 ; ; b = 7.6 ; ; c = 7.78 ; ;

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

p = a+b+c = 8.3+7.6+7.78 = 23.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.68 }{ 2 } = 11.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.84 * (11.84-8.3)(11.84-7.6)(11.84-7.78) } ; ; T = sqrt{ 721.52 } = 26.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.86 }{ 8.3 } = 6.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.86 }{ 7.6 } = 7.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.86 }{ 7.78 } = 6.91 ; ;

5. 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{ 8.3**2-7.6**2-7.78**2 }{ 2 * 7.6 * 7.78 } ) = 65° 18'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.6**2-8.3**2-7.78**2 }{ 2 * 8.3 * 7.78 } ) = 56° 17'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.78**2-8.3**2-7.6**2 }{ 2 * 7.6 * 8.3 } ) = 58° 23'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.86 }{ 11.84 } = 2.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.3 }{ 2 * sin 65° 18'32" } = 4.57 ; ;

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