6 14 17 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 14   c = 17

Area: T = 39.50987015732
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 19.39105704897° = 19°23'26″ = 0.33884292989 rad
Angle ∠ B = β = 50.77660676014° = 50°46'34″ = 0.88662095609 rad
Angle ∠ C = γ = 109.8333361909° = 109°50' = 1.91769537938 rad

Height: ha = 13.17695671911
Height: hb = 5.64441002247
Height: hc = 4.6488082538

Median: ma = 15.28107067899
Median: mb = 10.65436378763
Median: mc = 6.61443782777

Inradius: r = 2.13656054904
Circumradius: R = 9.03659841196

Vertex coordinates: A[17; 0] B[0; 0] C[3.79441176471; 4.6488082538]
Centroid: CG[6.9311372549; 1.5499360846]
Coordinates of the circumscribed circle: U[8.5; -3.06657803263]
Coordinates of the inscribed circle: I[4.5; 2.13656054904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.609942951° = 160°36'34″ = 0.33884292989 rad
∠ B' = β' = 129.2243932399° = 129°13'26″ = 0.88662095609 rad
∠ C' = γ' = 70.16766380911° = 70°10' = 1.91769537938 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 = 14 ; ; c = 17 ; ;

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

p = a+b+c = 6+14+17 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-6)(18.5-14)(18.5-17) } ; ; T = sqrt{ 1560.94 } = 39.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.51 }{ 6 } = 13.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.51 }{ 14 } = 5.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.51 }{ 17 } = 4.65 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 14**2+17**2-6**2 }{ 2 * 14 * 17 } ) = 19° 23'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+17**2-14**2 }{ 2 * 6 * 17 } ) = 50° 46'34" ; ; gamma = 180° - alpha - beta = 180° - 19° 23'26" - 50° 46'34" = 109° 50' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.51 }{ 18.5 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 19° 23'26" } = 9.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 17**2 - 6**2 } }{ 2 } = 15.281 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 6**2 - 14**2 } }{ 2 } = 10.654 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 6**2 - 17**2 } }{ 2 } = 6.614 ; ;
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