Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 46.39   b = 49.09   c = 9.49

Area: T = 216.0899329383
Perimeter: p = 104.97
Semiperimeter: s = 52.485

Angle ∠ A = α = 68.07879370569° = 68°4'41″ = 1.18881841496 rad
Angle ∠ B = β = 100.9822232917° = 100°58'56″ = 1.76224724504 rad
Angle ∠ C = γ = 10.94398300259° = 10°56'23″ = 0.19109360536 rad

Height: ha = 9.31662030344
Height: hb = 8.80438023786
Height: hc = 45.54404276886

Median: ma = 26.6822130256
Median: mb = 22.77325509111
Median: mc = 47.52327847985

Inradius: r = 4.11771635588
Circumradius: R = 25.00328954007

Vertex coordinates: A[9.49; 0] B[0; 0] C[-8.83875079031; 45.54404276886]
Centroid: CG[0.21774973656; 15.18801425629]
Coordinates of the circumscribed circle: U[4.745; 24.54985183548]
Coordinates of the inscribed circle: I[3.395; 4.11771635588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.9222062943° = 111°55'19″ = 1.18881841496 rad
∠ B' = β' = 79.01877670827° = 79°1'4″ = 1.76224724504 rad
∠ C' = γ' = 169.0660169974° = 169°3'37″ = 0.19109360536 rad

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How did we calculate this triangle?

a = 46.39 ; ; b = 49.09 ; ; c = 9.49 ; ;

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

p = a+b+c = 46.39+49.09+9.49 = 104.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 104.97 }{ 2 } = 52.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.49 * (52.49-46.39)(52.49-49.09)(52.49-9.49) } ; ; T = sqrt{ 46694.6 } = 216.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 216.09 }{ 46.39 } = 9.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 216.09 }{ 49.09 } = 8.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 216.09 }{ 9.49 } = 45.54 ; ;

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{ 49.09**2+9.49**2-46.39**2 }{ 2 * 49.09 * 9.49 } ) = 68° 4'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 46.39**2+9.49**2-49.09**2 }{ 2 * 46.39 * 9.49 } ) = 100° 58'56" ; ; gamma = 180° - alpha - beta = 180° - 68° 4'41" - 100° 58'56" = 10° 56'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 216.09 }{ 52.49 } = 4.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 46.39 }{ 2 * sin 68° 4'41" } = 25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 49.09**2+2 * 9.49**2 - 46.39**2 } }{ 2 } = 26.682 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.49**2+2 * 46.39**2 - 49.09**2 } }{ 2 } = 22.773 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 49.09**2+2 * 46.39**2 - 9.49**2 } }{ 2 } = 47.523 ; ;
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