Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 200   b = 190   c = 13.31

Area: T = 855.9276914821
Perimeter: p = 403.31
Semiperimeter: s = 201.655

Angle ∠ A = α = 137.3976854607° = 137°23'49″ = 2.39880274948 rad
Angle ∠ B = β = 40.02111663294° = 40°1'16″ = 0.69985011229 rad
Angle ∠ C = γ = 2.58219790632° = 2°34'55″ = 0.04550640359 rad

Height: ha = 8.55992691482
Height: hb = 9.01097569981
Height: hc = 128.6144111919

Median: ma = 90.21440679163
Median: mb = 105.1843544578
Median: mc = 194.9510534688

Inradius: r = 4.24545112436
Circumradius: R = 147.7298734557

Vertex coordinates: A[13.31; 0] B[0; 0] C[153.1611386176; 128.6144111919]
Centroid: CG[55.49904620586; 42.87113706397]
Coordinates of the circumscribed circle: U[6.655; 147.5798758597]
Coordinates of the inscribed circle: I[11.655; 4.24545112436]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.60331453926° = 42°36'11″ = 2.39880274948 rad
∠ B' = β' = 139.9798833671° = 139°58'44″ = 0.69985011229 rad
∠ C' = γ' = 177.4188020937° = 177°25'5″ = 0.04550640359 rad

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How did we calculate this triangle?

a = 200 ; ; b = 190 ; ; c = 13.31 ; ;

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

p = a+b+c = 200+190+13.31 = 403.31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 403.31 }{ 2 } = 201.66 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 201.66 * (201.66-200)(201.66-190)(201.66-13.31) } ; ; T = sqrt{ 732610.88 } = 855.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 855.93 }{ 200 } = 8.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 855.93 }{ 190 } = 9.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 855.93 }{ 13.31 } = 128.61 ; ;

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{ 190**2+13.31**2-200**2 }{ 2 * 190 * 13.31 } ) = 137° 23'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+13.31**2-190**2 }{ 2 * 200 * 13.31 } ) = 40° 1'16" ; ; gamma = 180° - alpha - beta = 180° - 137° 23'49" - 40° 1'16" = 2° 34'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 855.93 }{ 201.66 } = 4.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 137° 23'49" } = 147.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 190**2+2 * 13.31**2 - 200**2 } }{ 2 } = 90.214 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.31**2+2 * 200**2 - 190**2 } }{ 2 } = 105.184 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 190**2+2 * 200**2 - 13.31**2 } }{ 2 } = 194.951 ; ;
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