4 14 17 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 14   c = 17

Area: T = 20.33331625676
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 9.83882269853° = 9°50'18″ = 0.17217094535 rad
Angle ∠ B = β = 36.7299236457° = 36°43'45″ = 0.64110461079 rad
Angle ∠ C = γ = 133.4332536558° = 133°25'57″ = 2.32988370922 rad

Height: ha = 10.16765812838
Height: hb = 2.90547375097
Height: hc = 2.39221367727

Median: ma = 15.44334452115
Median: mb = 10.17334949747
Median: mc = 5.80994750193

Inradius: r = 1.16218950039
Circumradius: R = 11.70550163352

Vertex coordinates: A[17; 0] B[0; 0] C[3.20658823529; 2.39221367727]
Centroid: CG[6.73552941176; 0.79773789242]
Coordinates of the circumscribed circle: U[8.5; -8.04771987305]
Coordinates of the inscribed circle: I[3.5; 1.16218950039]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1621773015° = 170°9'42″ = 0.17217094535 rad
∠ B' = β' = 143.2710763543° = 143°16'15″ = 0.64110461079 rad
∠ C' = γ' = 46.56774634422° = 46°34'3″ = 2.32988370922 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 = 4 ; ; b = 14 ; ; c = 17 ; ;

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

p = a+b+c = 4+14+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 * (17.5-4)(17.5-14)(17.5-17) } ; ; T = sqrt{ 413.44 } = 20.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.33 }{ 4 } = 10.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.33 }{ 14 } = 2.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.33 }{ 17 } = 2.39 ; ;

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**2+17**2-4**2 }{ 2 * 14 * 17 } ) = 9° 50'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+17**2-14**2 }{ 2 * 4 * 17 } ) = 36° 43'45" ; ; gamma = 180° - alpha - beta = 180° - 9° 50'18" - 36° 43'45" = 133° 25'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.33 }{ 17.5 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 9° 50'18" } = 11.71 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 17**2 - 4**2 } }{ 2 } = 15.443 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 4**2 - 14**2 } }{ 2 } = 10.173 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 4**2 - 17**2 } }{ 2 } = 5.809 ; ;
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