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

Calculate another triangle




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 13.3 ; ; b = 10.8 ; ; c = 6.8 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 13.3**2-10.8**2-6.8**2 }{ 2 * 10.8 * 6.8 } ) = 95° 28'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.8**2-13.3**2-6.8**2 }{ 2 * 13.3 * 6.8 } ) = 53° 55'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.8**2-13.3**2-10.8**2 }{ 2 * 10.8 * 13.3 } ) = 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 ; ;




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