Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 270   b = 260   c = 109.46

Area: T = 14131.42111039
Perimeter: p = 639.46
Semiperimeter: s = 319.73

Angle ∠ A = α = 83.25987608636° = 83°15'32″ = 1.45331395082 rad
Angle ∠ B = β = 733.0001338708° = 73° = 1.27440926904 rad
Angle ∠ C = γ = 23.74111052656° = 23°44'28″ = 0.41443604549 rad

Height: ha = 104.6777193362
Height: hb = 108.7033239261
Height: hc = 258.2022468552

Median: ma = 146.8532803174
Median: mb = 159.8154723352
Median: mc = 259.3354970839

Inradius: r = 44.19879829978
Circumradius: R = 135.9439831237

Vertex coordinates: A[109.46; 0] B[0; 0] C[78.94397569889; 258.2022468552]
Centroid: CG[62.87999189963; 86.06774895175]
Coordinates of the circumscribed circle: U[54.73; 124.4365785917]
Coordinates of the inscribed circle: I[59.73; 44.19879829978]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 96.74112391364° = 96°44'28″ = 1.45331395082 rad
∠ B' = β' = 1076.999866129° = 107° = 1.27440926904 rad
∠ C' = γ' = 156.2598894734° = 156°15'32″ = 0.41443604549 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 = 270+260+109.46 = 639.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 639.46 }{ 2 } = 319.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 319.73 * (319.73-270)(319.73-260)(319.73-109.46) } ; ; T = sqrt{ 199697062.41 } = 14131.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14131.42 }{ 270 } = 104.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14131.42 }{ 260 } = 108.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14131.42 }{ 109.46 } = 258.2 ; ;

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{ 260**2+109.46**2-270**2 }{ 2 * 260 * 109.46 } ) = 83° 15'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 270**2+109.46**2-260**2 }{ 2 * 270 * 109.46 } ) = 73° ; ;
 gamma = 180° - alpha - beta = 180° - 83° 15'32" - 73° = 23° 44'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14131.42 }{ 319.73 } = 44.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 270 }{ 2 * sin 83° 15'32" } = 135.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 260**2+2 * 109.46**2 - 270**2 } }{ 2 } = 146.853 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 109.46**2+2 * 270**2 - 260**2 } }{ 2 } = 159.815 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 260**2+2 * 270**2 - 109.46**2 } }{ 2 } = 259.335 ; ;
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