5.39 7.07 6.4 triangle

Acute scalene triangle.

Sides: a = 5.39   b = 7.07   c = 6.4

Area: T = 16.50553160454
Perimeter: p = 18.86
Semiperimeter: s = 9.43

Angle ∠ A = α = 46.84985964847° = 46°50'55″ = 0.81876622586 rad
Angle ∠ B = β = 73.12551045339° = 73°7'30″ = 1.276627384 rad
Angle ∠ C = γ = 60.02662989814° = 60°1'35″ = 1.0487656555 rad

Height: ha = 6.12444215382
Height: hb = 4.66991134499
Height: hc = 5.15879112642

Median: ma = 6.18113772737
Median: mb = 4.74444520232
Median: mc = 5.41109610976

Inradius: r = 1.75502986262
Circumradius: R = 3.69440631632

Vertex coordinates: A[6.4; 0] B[0; 0] C[1.5654625; 5.15879112642]
Centroid: CG[2.6554875; 1.71993037547]
Coordinates of the circumscribed circle: U[3.2; 1.84655629638]
Coordinates of the inscribed circle: I[2.36; 1.75502986262]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.1511403515° = 133°9'5″ = 0.81876622586 rad
∠ B' = β' = 106.8754895466° = 106°52'30″ = 1.276627384 rad
∠ C' = γ' = 119.9743701019° = 119°58'25″ = 1.0487656555 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 = 5.39+7.07+6.4 = 18.86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.86 }{ 2 } = 9.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.43 * (9.43-5.39)(9.43-7.07)(9.43-6.4) } ; ; T = sqrt{ 272.43 } = 16.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.51 }{ 5.39 } = 6.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.51 }{ 7.07 } = 4.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.51 }{ 6.4 } = 5.16 ; ;

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{ 7.07**2+6.4**2-5.39**2 }{ 2 * 7.07 * 6.4 } ) = 46° 50'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.39**2+6.4**2-7.07**2 }{ 2 * 5.39 * 6.4 } ) = 73° 7'30" ; ;
 gamma = 180° - alpha - beta = 180° - 46° 50'55" - 73° 7'30" = 60° 1'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.51 }{ 9.43 } = 1.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.39 }{ 2 * sin 46° 50'55" } = 3.69 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 6.4**2 - 5.39**2 } }{ 2 } = 6.181 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 5.39**2 - 7.07**2 } }{ 2 } = 4.744 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 5.39**2 - 6.4**2 } }{ 2 } = 5.411 ; ;
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