Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 0.26   b = 0.3   c = 0.33

Area: T = 0.03770509025
Perimeter: p = 0.89
Semiperimeter: s = 0.445

Angle ∠ A = α = 48.46108759577° = 48°27'39″ = 0.84658018439 rad
Angle ∠ B = β = 59.73297497456° = 59°43'47″ = 1.04224807945 rad
Angle ∠ C = γ = 71.80993742967° = 71°48'34″ = 1.25333100153 rad

Height: ha = 0.28550069422
Height: hb = 0.24770060166
Height: hc = 0.22545509242

Median: ma = 0.2877315158
Median: mb = 0.25664176281
Median: mc = 0.2277101299

Inradius: r = 0.0833260455
Circumradius: R = 0.17436799799

Vertex coordinates: A[0.33; 0] B[0; 0] C[0.13110606061; 0.22545509242]
Centroid: CG[0.15436868687; 0.07548503081]
Coordinates of the circumscribed circle: U[0.165; 0.05442193271]
Coordinates of the inscribed circle: I[0.145; 0.0833260455]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.5399124042° = 131°32'21″ = 0.84658018439 rad
∠ B' = β' = 120.2770250254° = 120°16'13″ = 1.04224807945 rad
∠ C' = γ' = 108.1910625703° = 108°11'26″ = 1.25333100153 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 = 0.26+0.3+0.33 = 0.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.89 }{ 2 } = 0.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.45 * (0.45-0.26)(0.45-0.3)(0.45-0.33) } ; ; T = sqrt{ 0 } = 0.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.04 }{ 0.26 } = 0.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.04 }{ 0.3 } = 0.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.04 }{ 0.33 } = 0.22 ; ;

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{ 0.3**2+0.33**2-0.26**2 }{ 2 * 0.3 * 0.33 } ) = 48° 27'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.26**2+0.33**2-0.3**2 }{ 2 * 0.26 * 0.33 } ) = 59° 43'47" ; ;
 gamma = 180° - alpha - beta = 180° - 48° 27'39" - 59° 43'47" = 71° 48'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.04 }{ 0.45 } = 0.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.26 }{ 2 * sin 48° 27'39" } = 0.17 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.3**2+2 * 0.33**2 - 0.26**2 } }{ 2 } = 0.287 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.33**2+2 * 0.26**2 - 0.3**2 } }{ 2 } = 0.256 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.3**2+2 * 0.26**2 - 0.33**2 } }{ 2 } = 0.227 ; ;
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