12.7 9.9 9.31 triangle

Acute scalene triangle.

Sides: a = 12.7   b = 9.9   c = 9.31

Area: T = 45.71218151773
Perimeter: p = 31.91
Semiperimeter: s = 15.955

Angle ∠ A = α = 82.7088377834° = 82°42'30″ = 1.44435335122 rad
Angle ∠ B = β = 50.64442480173° = 50°38'39″ = 0.88439088751 rad
Angle ∠ C = γ = 46.64773741486° = 46°38'51″ = 0.81441502663 rad

Height: ha = 7.19987110515
Height: hb = 9.23547101368
Height: hc = 9.82199388136

Median: ma = 7.21325272963
Median: mb = 9.97439936836
Median: mc = 10.39113894644

Inradius: r = 2.86550463916
Circumradius: R = 6.4021771049

Vertex coordinates: A[9.31; 0] B[0; 0] C[8.05334962406; 9.82199388136]
Centroid: CG[5.78878320802; 3.27333129379]
Coordinates of the circumscribed circle: U[4.655; 4.39547295212]
Coordinates of the inscribed circle: I[6.055; 2.86550463916]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 97.2921622166° = 97°17'30″ = 1.44435335122 rad
∠ B' = β' = 129.3565751983° = 129°21'21″ = 0.88439088751 rad
∠ C' = γ' = 133.3532625851° = 133°21'9″ = 0.81441502663 rad

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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 = 12.7 ; ; b = 9.9 ; ; c = 9.31 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 12.7+9.9+9.31 = 31.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.91 }{ 2 } = 15.96 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.96 * (15.96-12.7)(15.96-9.9)(15.96-9.31) } ; ; T = sqrt{ 2089.57 } = 45.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.71 }{ 12.7 } = 7.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.71 }{ 9.9 } = 9.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.71 }{ 9.31 } = 9.82 ; ;

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{ 9.9**2+9.31**2-12.7**2 }{ 2 * 9.9 * 9.31 } ) = 82° 42'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.7**2+9.31**2-9.9**2 }{ 2 * 12.7 * 9.31 } ) = 50° 38'39" ; ;
 gamma = 180° - alpha - beta = 180° - 82° 42'30" - 50° 38'39" = 46° 38'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.71 }{ 15.96 } = 2.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.7 }{ 2 * sin 82° 42'30" } = 6.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.9**2+2 * 9.31**2 - 12.7**2 } }{ 2 } = 7.213 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.31**2+2 * 12.7**2 - 9.9**2 } }{ 2 } = 9.974 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.9**2+2 * 12.7**2 - 9.31**2 } }{ 2 } = 10.391 ; ;
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