6 13 16 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 13   c = 16

Area: T = 36.85769871259
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 20.75663151734° = 20°45'23″ = 0.36222660404 rad
Angle ∠ B = β = 50.1621560023° = 50°9'42″ = 0.87554843803 rad
Angle ∠ C = γ = 109.0822124804° = 109°4'56″ = 1.90438422329 rad

Height: ha = 12.28656623753
Height: hb = 5.67703057117
Height: hc = 4.60771233907

Median: ma = 14.26553426177
Median: mb = 10.18657743937
Median: mc = 6.2054836823

Inradius: r = 2.10661135501
Circumradius: R = 8.46551520466

Vertex coordinates: A[16; 0] B[0; 0] C[3.844375; 4.60771233907]
Centroid: CG[6.61545833333; 1.53657077969]
Coordinates of the circumscribed circle: U[8; -2.76774535537]
Coordinates of the inscribed circle: I[4.5; 2.10661135501]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.2443684827° = 159°14'37″ = 0.36222660404 rad
∠ B' = β' = 129.8388439977° = 129°50'18″ = 0.87554843803 rad
∠ C' = γ' = 70.91878751964° = 70°55'4″ = 1.90438422329 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 = 6 ; ; b = 13 ; ; c = 16 ; ;

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

p = a+b+c = 6+13+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-6)(17.5-13)(17.5-16) } ; ; T = sqrt{ 1358.44 } = 36.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.86 }{ 6 } = 12.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.86 }{ 13 } = 5.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.86 }{ 16 } = 4.61 ; ;

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{ 6**2-13**2-16**2 }{ 2 * 13 * 16 } ) = 20° 45'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-6**2-16**2 }{ 2 * 6 * 16 } ) = 50° 9'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-6**2-13**2 }{ 2 * 13 * 6 } ) = 109° 4'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.86 }{ 17.5 } = 2.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 20° 45'23" } = 8.47 ; ;




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