6 13 17 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 13   c = 17

Area: T = 32.86333534503
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 17.30218627088° = 17°18'7″ = 0.3021974471 rad
Angle ∠ B = β = 40.11991668984° = 40°7'9″ = 0.77002115555 rad
Angle ∠ C = γ = 122.5798970393° = 122°34'44″ = 2.13994066271 rad

Height: ha = 10.95444511501
Height: hb = 5.05659005308
Height: hc = 3.86662768765

Median: ma = 14.83223969742
Median: mb = 10.96658560997
Median: mc = 5.5

Inradius: r = 1.82657418584
Circumradius: R = 10.08772237674

Vertex coordinates: A[17; 0] B[0; 0] C[4.58882352941; 3.86662768765]
Centroid: CG[7.19660784314; 1.28987589588]
Coordinates of the circumscribed circle: U[8.5; -5.43215820286]
Coordinates of the inscribed circle: I[5; 1.82657418584]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6988137291° = 162°41'53″ = 0.3021974471 rad
∠ B' = β' = 139.8810833102° = 139°52'51″ = 0.77002115555 rad
∠ C' = γ' = 57.42110296072° = 57°25'16″ = 2.13994066271 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 = 17 ; ;

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

p = a+b+c = 6+13+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-6)(18-13)(18-17) } ; ; T = sqrt{ 1080 } = 32.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.86 }{ 6 } = 10.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.86 }{ 13 } = 5.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.86 }{ 17 } = 3.87 ; ;

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**2-17**2 }{ 2 * 13 * 17 } ) = 17° 18'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-6**2-17**2 }{ 2 * 6 * 17 } ) = 40° 7'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-6**2-13**2 }{ 2 * 13 * 6 } ) = 122° 34'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.86 }{ 18 } = 1.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 17° 18'7" } = 10.09 ; ;




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