Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 24.73   b = 49   c = 48

Area: T = 579.4110830984
Perimeter: p = 121.73
Semiperimeter: s = 60.865

Angle ∠ A = α = 29.51879551448° = 29°31'5″ = 0.51551855057 rad
Angle ∠ B = β = 77.4822004775° = 77°28'55″ = 1.35223160944 rad
Angle ∠ C = γ = 733.0000400802° = 73° = 1.27440910535 rad

Height: ha = 46.85989430638
Height: hb = 23.64994216728
Height: hc = 24.14221179577

Median: ma = 46.98999656183
Median: mb = 29.28437232947
Median: mc = 30.50105975351

Inradius: r = 9.52196061938
Circumradius: R = 25.09765967883

Vertex coordinates: A[48; 0] B[0; 0] C[5.3660134375; 24.14221179577]
Centroid: CG[17.78767114583; 8.04773726526]
Coordinates of the circumscribed circle: U[24; 7.3387517997]
Coordinates of the inscribed circle: I[11.865; 9.52196061938]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4822044855° = 150°28'55″ = 0.51551855057 rad
∠ B' = β' = 102.5187995225° = 102°31'5″ = 1.35223160944 rad
∠ C' = γ' = 1076.99995992° = 107° = 1.27440910535 rad

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How did we calculate this triangle?

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

p = a+b+c = 24.73+49+48 = 121.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 121.73 }{ 2 } = 60.87 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60.87 * (60.87-24.73)(60.87-49)(60.87-48) } ; ; T = sqrt{ 335716.91 } = 579.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 579.41 }{ 24.73 } = 46.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 579.41 }{ 49 } = 23.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 579.41 }{ 48 } = 24.14 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 49**2+48**2-24.73**2 }{ 2 * 49 * 48 } ) = 29° 31'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.73**2+48**2-49**2 }{ 2 * 24.73 * 48 } ) = 77° 28'55" ; ;
 gamma = 180° - alpha - beta = 180° - 29° 31'5" - 77° 28'55" = 73° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 579.41 }{ 60.87 } = 9.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.73 }{ 2 * sin 29° 31'5" } = 25.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 49**2+2 * 48**2 - 24.73**2 } }{ 2 } = 46.9 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 24.73**2 - 49**2 } }{ 2 } = 29.284 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 49**2+2 * 24.73**2 - 48**2 } }{ 2 } = 30.501 ; ;
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