Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.52   b = 356   c = 354.7

Area: T = 581.1943841296
Perimeter: p = 714.22
Semiperimeter: s = 357.11

Angle ∠ A = α = 0.52774345546° = 0°31'39″ = 0.00992054696 rad
Angle ∠ B = β = 111.4109615469° = 111°24'35″ = 1.94444646083 rad
Angle ∠ C = γ = 68.06329499761° = 68°3'47″ = 1.18879225757 rad

Height: ha = 330.2243773463
Height: hb = 3.26551339399
Height: hc = 3.27771008813

Median: ma = 355.3466235945
Median: mb = 176.715513857
Median: mc = 178.6654973344

Inradius: r = 1.62774924849
Circumradius: R = 191.1933381802

Vertex coordinates: A[354.7; 0] B[0; 0] C[-1.28549162673; 3.27771008813]
Centroid: CG[117.8055027911; 1.09223669604]
Coordinates of the circumscribed circle: U[177.35; 71.42774929212]
Coordinates of the inscribed circle: I[1.11; 1.62774924849]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.4732565445° = 179°28'21″ = 0.00992054696 rad
∠ B' = β' = 68.59903845307° = 68°35'25″ = 1.94444646083 rad
∠ C' = γ' = 111.9377050024° = 111°56'13″ = 1.18879225757 rad

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How did we calculate this triangle?

a = 3.52 ; ; b = 356 ; ; c = 354.7 ; ;

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

p = a+b+c = 3.52+356+354.7 = 714.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 714.22 }{ 2 } = 357.11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 357.11 * (357.11-3.52)(357.11-356)(357.11-354.7) } ; ; T = sqrt{ 337786.28 } = 581.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 581.19 }{ 3.52 } = 330.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 581.19 }{ 356 } = 3.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 581.19 }{ 354.7 } = 3.28 ; ;

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{ 3.52**2-356**2-354.7**2 }{ 2 * 356 * 354.7 } ) = 0° 31'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 356**2-3.52**2-354.7**2 }{ 2 * 3.52 * 354.7 } ) = 111° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 354.7**2-3.52**2-356**2 }{ 2 * 356 * 3.52 } ) = 68° 3'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 581.19 }{ 357.11 } = 1.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.52 }{ 2 * sin 0° 31'39" } = 191.19 ; ;

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