Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 5.4   b = 9.3   c = 10.75

Area: T = 25.11099904716
Perimeter: p = 25.45
Semiperimeter: s = 12.725

Angle ∠ A = α = 30.15439662375° = 30°9'14″ = 0.52662859934 rad
Angle ∠ B = β = 59.89659479534° = 59°53'45″ = 1.04553815004 rad
Angle ∠ C = γ = 89.9550085809° = 89°57' = 1.57699251598 rad

Height: ha = 9.3299996471
Height: hb = 5.43999979509
Height: hc = 4.67216261343

Median: ma = 9.68217482925
Median: mb = 7.12331137854
Median: mc = 5.37990682279

Inradius: r = 1.97332801942
Circumradius: R = 5.37550020396

Vertex coordinates: A[10.75; 0] B[0; 0] C[2.70884883721; 4.67216261343]
Centroid: CG[4.48661627907; 1.55772087114]
Coordinates of the circumscribed circle: U[5.375; 0.00546825237]
Coordinates of the inscribed circle: I[3.425; 1.97332801942]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.8466033762° = 149°50'46″ = 0.52662859934 rad
∠ B' = β' = 120.1044052047° = 120°6'15″ = 1.04553815004 rad
∠ C' = γ' = 90.0549914191° = 90°3' = 1.57699251598 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 = 5.4+9.3+10.75 = 25.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.45 }{ 2 } = 12.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.73 * (12.73-5.4)(12.73-9.3)(12.73-10.75) } ; ; T = sqrt{ 630.51 } = 25.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.11 }{ 5.4 } = 9.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.11 }{ 9.3 } = 5.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.11 }{ 10.75 } = 4.67 ; ;

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{ 9.3**2+10.75**2-5.4**2 }{ 2 * 9.3 * 10.75 } ) = 30° 9'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.4**2+10.75**2-9.3**2 }{ 2 * 5.4 * 10.75 } ) = 59° 53'45" ; ; gamma = 180° - alpha - beta = 180° - 30° 9'14" - 59° 53'45" = 89° 57' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.11 }{ 12.73 } = 1.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.4 }{ 2 * sin 30° 9'14" } = 5.38 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.3**2+2 * 10.75**2 - 5.4**2 } }{ 2 } = 9.682 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.75**2+2 * 5.4**2 - 9.3**2 } }{ 2 } = 7.123 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.3**2+2 * 5.4**2 - 10.75**2 } }{ 2 } = 5.379 ; ;
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