Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 311.26   b = 140   c = 278

Area: T = 194609.9999976
Perimeter: p = 729.26
Semiperimeter: s = 364.63

Angle ∠ A = α = 89.99991075873° = 89°59'57″ = 1.57107807513 rad
Angle ∠ B = β = 26.73298743053° = 26°43'48″ = 0.46765243153 rad
Angle ∠ C = γ = 63.27110181074° = 63°16'16″ = 1.10442875871 rad

Height: ha = 125.0440159337
Height: hb = 2787.999999966
Height: hc = 1409.999999983

Median: ma = 155.6321947556
Median: mb = 286.6766461887
Median: mc = 197.2832522794

Inradius: r = 53.36991687399
Circumradius: R = 155.6330000019

Vertex coordinates: A[278; 0] B[0; 0] C[277.9987819424; 1409.999999983]
Centroid: CG[185.3332606475; 46.6676666661]
Coordinates of the circumscribed circle: U[139; 69.99878350085]
Coordinates of the inscribed circle: I[224.63; 53.36991687399]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.00108924127° = 90°3″ = 1.57107807513 rad
∠ B' = β' = 153.2770125695° = 153°16'12″ = 0.46765243153 rad
∠ C' = γ' = 116.7298981893° = 116°43'44″ = 1.10442875871 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 = 311.26+140+278 = 729.26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 729.26 }{ 2 } = 364.63 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 364.63 * (364.63-311.26)(364.63-140)(364.63-278) } ; ; T = sqrt{ 378691599.91 } = 19460 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19460 }{ 311.26 } = 125.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19460 }{ 140 } = 278 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19460 }{ 278 } = 140 ; ;

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{ 140**2+278**2-311.26**2 }{ 2 * 140 * 278 } ) = 89° 59'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 311.26**2+278**2-140**2 }{ 2 * 311.26 * 278 } ) = 26° 43'48" ; ; gamma = 180° - alpha - beta = 180° - 89° 59'57" - 26° 43'48" = 63° 16'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19460 }{ 364.63 } = 53.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 311.26 }{ 2 * sin 89° 59'57" } = 155.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 278**2 - 311.26**2 } }{ 2 } = 155.632 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 278**2+2 * 311.26**2 - 140**2 } }{ 2 } = 286.676 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 311.26**2 - 278**2 } }{ 2 } = 197.283 ; ;
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