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: h_a = 13.17695671911
Height: h_b = 5.64441002247
Height: h_c = 4.6488082538

Median: m_a = 15.28107067899
Median: m_b = 10.65436378763
Median: m_c = 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

Calculate another triangle

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

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

6. Inradius

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

7. Circumradius

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

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