5 13 17 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 13   c = 17

Area: T = 22.18552991866
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 11.5822103507° = 11°34'56″ = 0.20221458405 rad
Angle ∠ B = β = 31.46769762933° = 31°28'1″ = 0.5499202342 rad
Angle ∠ C = γ = 136.95109202° = 136°57'3″ = 2.39902444711 rad

Height: ha = 8.87441196746
Height: hb = 3.41331229518
Height: hc = 2.61100351984

Median: ma = 14.92548115566
Median: mb = 10.71221426428
Median: mc = 4.97549371855

Inradius: r = 1.26877313821
Circumradius: R = 12.4521939353

Vertex coordinates: A[17; 0] B[0; 0] C[4.26547058824; 2.61100351984]
Centroid: CG[7.08882352941; 0.87700117328]
Coordinates of the circumscribed circle: U[8.5; -9.09994941426]
Coordinates of the inscribed circle: I[4.5; 1.26877313821]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.4187896493° = 168°25'4″ = 0.20221458405 rad
∠ B' = β' = 148.5333023707° = 148°31'59″ = 0.5499202342 rad
∠ C' = γ' = 43.04990798002° = 43°2'57″ = 2.39902444711 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 = 5 ; ; b = 13 ; ; c = 17 ; ;

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

p = a+b+c = 5+13+17 = 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 * (17.5-5)(17.5-13)(17.5-17) } ; ; T = sqrt{ 492.19 } = 22.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.19 }{ 5 } = 8.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.19 }{ 13 } = 3.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.19 }{ 17 } = 2.61 ; ;

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{ 5**2-13**2-17**2 }{ 2 * 13 * 17 } ) = 11° 34'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-5**2-17**2 }{ 2 * 5 * 17 } ) = 31° 28'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-5**2-13**2 }{ 2 * 13 * 5 } ) = 136° 57'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.19 }{ 17.5 } = 1.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 34'56" } = 12.45 ; ;




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