Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 66.23   b = 121   c = 164

Area: T = 3490.802239814
Perimeter: p = 351.23
Semiperimeter: s = 175.615

Angle ∠ A = α = 20.59989485632° = 20°35'56″ = 0.36595194749 rad
Angle ∠ B = β = 39.99988001882° = 39°59'56″ = 0.69881107601 rad
Angle ∠ C = γ = 119.4022251249° = 119°24'8″ = 2.08439624186 rad

Height: ha = 105.4154537162
Height: hb = 57.69992131923
Height: hc = 42.57107609529

Median: ma = 140.2576539152
Median: mb = 109.4587555472
Median: mc = 52.81876717586

Inradius: r = 19.87875867559
Circumradius: R = 94.12436405061

Vertex coordinates: A[164; 0] B[0; 0] C[50.7366014939; 42.57107609529]
Centroid: CG[71.57986716463; 14.1990253651]
Coordinates of the circumscribed circle: U[82; -46.20988703835]
Coordinates of the inscribed circle: I[54.615; 19.87875867559]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.4011051437° = 159°24'4″ = 0.36595194749 rad
∠ B' = β' = 140.0011199812° = 140°4″ = 0.69881107601 rad
∠ C' = γ' = 60.59877487514° = 60°35'52″ = 2.08439624186 rad

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How did we calculate this triangle?

a = 66.23 ; ; b = 121 ; ; c = 164 ; ;

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

p = a+b+c = 66.23+121+164 = 351.23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 351.23 }{ 2 } = 175.62 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 175.62 * (175.62-66.23)(175.62-121)(175.62-164) } ; ; T = sqrt{ 12185701.38 } = 3490.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3490.8 }{ 66.23 } = 105.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3490.8 }{ 121 } = 57.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3490.8 }{ 164 } = 42.57 ; ;

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{ 66.23**2-121**2-164**2 }{ 2 * 121 * 164 } ) = 20° 35'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 121**2-66.23**2-164**2 }{ 2 * 66.23 * 164 } ) = 39° 59'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 164**2-66.23**2-121**2 }{ 2 * 121 * 66.23 } ) = 119° 24'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3490.8 }{ 175.62 } = 19.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 66.23 }{ 2 * sin 20° 35'56" } = 94.12 ; ;




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