6 16 17 triangle

Acute scalene triangle.

Sides: a = 6   b = 16   c = 17

Area: T = 47.99441402673
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 20.66546780584° = 20°39'53″ = 0.3610666671 rad
Angle ∠ B = β = 70.23106049282° = 70°13'50″ = 1.22657552917 rad
Angle ∠ C = γ = 89.10547170134° = 89°6'17″ = 1.55551706909 rad

Height: ha = 15.99880467558
Height: hb = 5.99992675334
Height: hc = 5.64663694432

Median: ma = 16.23326830807
Median: mb = 9.92547166206
Median: mc = 8.58877820187

Inradius: r = 2.46112379624
Circumradius: R = 8.50110377877

Vertex coordinates: A[17; 0] B[0; 0] C[2.02994117647; 5.64663694432]
Centroid: CG[6.34331372549; 1.88221231477]
Coordinates of the circumscribed circle: U[8.5; 0.13328287154]
Coordinates of the inscribed circle: I[3.5; 2.46112379624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.3355321942° = 159°20'7″ = 0.3610666671 rad
∠ B' = β' = 109.7699395072° = 109°46'10″ = 1.22657552917 rad
∠ C' = γ' = 90.89552829866° = 90°53'43″ = 1.55551706909 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 = 16 ; ; c = 17 ; ;

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

p = a+b+c = 6+16+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-6)(19.5-16)(19.5-17) } ; ; T = sqrt{ 2303.44 } = 47.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.99 }{ 6 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.99 }{ 16 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.99 }{ 17 } = 5.65 ; ;

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**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 20° 39'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-6**2-17**2 }{ 2 * 6 * 17 } ) = 70° 13'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-6**2-16**2 }{ 2 * 16 * 6 } ) = 89° 6'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.99 }{ 19.5 } = 2.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 20° 39'53" } = 8.5 ; ;




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