12.81 14.32 6.4 triangle

Obtuse scalene triangle.

Sides: a = 12.81   b = 14.32   c = 6.4

Area: T = 40.99219999697
Perimeter: p = 33.53
Semiperimeter: s = 16.765

Angle ∠ A = α = 63.45110808894° = 63°27'4″ = 1.10774302755 rad
Angle ∠ B = β = 90.0022201426° = 90°8″ = 1.57108347489 rad
Angle ∠ C = γ = 26.54767176847° = 26°32'48″ = 0.46333276292 rad

Height: ha = 6.43999999953
Height: hb = 5.72551396606
Height: hc = 12.81099999905

Median: ma = 9.05546769683
Median: mb = 7.16597800246
Median: mc = 13.20437589345

Inradius: r = 2.44550939439
Circumradius: R = 7.16600000053

Vertex coordinates: A[6.4; 0] B[0; 0] C[-00.0004921875; 12.81099999905]
Centroid: CG[2.13331692708; 4.27699999968]
Coordinates of the circumscribed circle: U[3.2; 6.40551229555]
Coordinates of the inscribed circle: I[2.445; 2.44550939439]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5498919111° = 116°32'56″ = 1.10774302755 rad
∠ B' = β' = 89.9987798574° = 89°59'52″ = 1.57108347489 rad
∠ C' = γ' = 153.4533282315° = 153°27'12″ = 0.46333276292 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 = 12.81 ; ; b = 14.32 ; ; c = 6.4 ; ;

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

p = a+b+c = 12.81+14.32+6.4 = 33.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.53 }{ 2 } = 16.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.77 * (16.77-12.81)(16.77-14.32)(16.77-6.4) } ; ; T = sqrt{ 1680.34 } = 40.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.99 }{ 12.81 } = 6.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.99 }{ 14.32 } = 5.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.99 }{ 6.4 } = 12.81 ; ;

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{ 14.32**2+6.4**2-12.81**2 }{ 2 * 14.32 * 6.4 } ) = 63° 27'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.81**2+6.4**2-14.32**2 }{ 2 * 12.81 * 6.4 } ) = 90° 8" ; ;
 gamma = 180° - alpha - beta = 180° - 63° 27'4" - 90° 8" = 26° 32'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.99 }{ 16.77 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.81 }{ 2 * sin 63° 27'4" } = 7.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.32**2+2 * 6.4**2 - 12.81**2 } }{ 2 } = 9.055 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 12.81**2 - 14.32**2 } }{ 2 } = 7.16 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.32**2+2 * 12.81**2 - 6.4**2 } }{ 2 } = 13.204 ; ;
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