12.8 11.4 3.3 triangle

Obtuse scalene triangle.

Sides: a = 12.8   b = 11.4   c = 3.3

Area: T = 17.91103976435
Perimeter: p = 27.5
Semiperimeter: s = 13.75

Angle ∠ A = α = 107.7921590573° = 107°47'30″ = 1.88113181615 rad
Angle ∠ B = β = 57.99880641654° = 57°59'53″ = 1.01222571795 rad
Angle ∠ C = γ = 14.21103452616° = 14°12'37″ = 0.24880173127 rad

Height: ha = 2.79884996318
Height: hb = 3.14221750252
Height: hc = 10.85547864506

Median: ma = 5.42881672782
Median: mb = 7.4087766195
Median: mc = 12.00773935556

Inradius: r = 1.30325743741
Circumradius: R = 6.72114588082

Vertex coordinates: A[3.3; 0] B[0; 0] C[6.78333333333; 10.85547864506]
Centroid: CG[3.36111111111; 3.61882621502]
Coordinates of the circumscribed circle: U[1.65; 6.51657891702]
Coordinates of the inscribed circle: I[2.35; 1.30325743741]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 72.2088409427° = 72°12'30″ = 1.88113181615 rad
∠ B' = β' = 122.0021935835° = 122°7″ = 1.01222571795 rad
∠ C' = γ' = 165.7989654738° = 165°47'23″ = 0.24880173127 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 = 12.8+11.4+3.3 = 27.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.5 }{ 2 } = 13.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.75 * (13.75-12.8)(13.75-11.4)(13.75-3.3) } ; ; T = sqrt{ 320.78 } = 17.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.91 }{ 12.8 } = 2.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.91 }{ 11.4 } = 3.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.91 }{ 3.3 } = 10.85 ; ;

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{ 11.4**2+3.3**2-12.8**2 }{ 2 * 11.4 * 3.3 } ) = 107° 47'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.8**2+3.3**2-11.4**2 }{ 2 * 12.8 * 3.3 } ) = 57° 59'53" ; ; gamma = 180° - alpha - beta = 180° - 107° 47'30" - 57° 59'53" = 14° 12'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.91 }{ 13.75 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.8 }{ 2 * sin 107° 47'30" } = 6.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.4**2+2 * 3.3**2 - 12.8**2 } }{ 2 } = 5.428 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.3**2+2 * 12.8**2 - 11.4**2 } }{ 2 } = 7.408 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.4**2+2 * 12.8**2 - 3.3**2 } }{ 2 } = 12.007 ; ;
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