6 17 22 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 17   c = 22

Area: T = 31.95221126062
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 9.83882269853° = 9°50'18″ = 0.17217094535 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 141.2076748643° = 141°12'24″ = 2.46545226899 rad

Height: ha = 10.65107042021
Height: hb = 3.75990720713
Height: hc = 2.90547375097

Median: ma = 19.42993592277
Median: mb = 13.7022189606
Median: mc = 6.44220493634

Inradius: r = 1.42200938936
Circumradius: R = 17.55875245028

Vertex coordinates: A[22; 0] B[0; 0] C[5.25; 2.90547375097]
Centroid: CG[9.08333333333; 0.96882458366]
Coordinates of the circumscribed circle: U[11; -13.68545411566]
Coordinates of the inscribed circle: I[5.5; 1.42200938936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1621773015° = 170°9'42″ = 0.17217094535 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 38.79332513571° = 38°47'36″ = 2.46545226899 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 = 17 ; ; c = 22 ; ;

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

p = a+b+c = 6+17+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-6)(22.5-17)(22.5-22) } ; ; T = sqrt{ 1020.94 } = 31.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.95 }{ 6 } = 10.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.95 }{ 17 } = 3.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.95 }{ 22 } = 2.9 ; ;

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**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 9° 50'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-6**2-22**2 }{ 2 * 6 * 22 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-6**2-17**2 }{ 2 * 17 * 6 } ) = 141° 12'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.95 }{ 22.5 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 9° 50'18" } = 17.56 ; ;




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