13.3 10.8 6.8 triangle

Obtuse scalene triangle.

Sides: a = 13.3   b = 10.8   c = 6.8

Area: T = 36.5532577115
Perimeter: p = 30.9
Semiperimeter: s = 15.45

Angle ∠ A = α = 95.4733421006° = 95°28'24″ = 1.66663255447 rad
Angle ∠ B = β = 53.93328603147° = 53°55'58″ = 0.94113059875 rad
Angle ∠ C = γ = 30.59437186793° = 30°35'37″ = 0.53439611214 rad

Height: ha = 5.49766281376
Height: hb = 6.7698995762
Height: hc = 10.7510757975

Median: ma = 6.10106147231
Median: mb = 9.07877199781
Median: mc = 11.62877684875

Inradius: r = 2.36658625964
Circumradius: R = 6.6880459198

Vertex coordinates: A[6.8; 0] B[0; 0] C[7.83301470588; 10.7510757975]
Centroid: CG[4.87767156863; 3.58435859917]
Coordinates of the circumscribed circle: U[3.4; 5.75105247671]
Coordinates of the inscribed circle: I[4.65; 2.36658625964]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 84.5276578994° = 84°31'36″ = 1.66663255447 rad
∠ B' = β' = 126.0677139685° = 126°4'2″ = 0.94113059875 rad
∠ C' = γ' = 149.4066281321° = 149°24'23″ = 0.53439611214 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 = 13.3+10.8+6.8 = 30.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30.9 }{ 2 } = 15.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.45 * (15.45-13.3)(15.45-10.8)(15.45-6.8) } ; ; T = sqrt{ 1336.09 } = 36.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.55 }{ 13.3 } = 5.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.55 }{ 10.8 } = 6.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.55 }{ 6.8 } = 10.75 ; ;

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{ 10.8**2+6.8**2-13.3**2 }{ 2 * 10.8 * 6.8 } ) = 95° 28'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.3**2+6.8**2-10.8**2 }{ 2 * 13.3 * 6.8 } ) = 53° 55'58" ; ; gamma = 180° - alpha - beta = 180° - 95° 28'24" - 53° 55'58" = 30° 35'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.55 }{ 15.45 } = 2.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.3 }{ 2 * sin 95° 28'24" } = 6.68 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.8**2+2 * 6.8**2 - 13.3**2 } }{ 2 } = 6.101 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.8**2+2 * 13.3**2 - 10.8**2 } }{ 2 } = 9.078 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.8**2+2 * 13.3**2 - 6.8**2 } }{ 2 } = 11.628 ; ;
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