6 17 18 triangle

Acute scalene triangle.

Sides: a = 6   b = 17   c = 18

Area: T = 50.99993872512
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 19.47109772519° = 19°28'16″ = 0.34398326616 rad
Angle ∠ B = β = 70.81098855373° = 70°48'36″ = 1.23658656456 rad
Angle ∠ C = γ = 89.71991372109° = 89°43'9″ = 1.56658943464 rad

Height: ha = 176.9997957504
Height: hb = 65.9999279119
Height: hc = 5.66765985835

Median: ma = 17.24881883107
Median: mb = 10.3880269746
Median: mc = 9.02877350426

Inradius: r = 2.48877749879
Circumradius: R = 99.0001081334

Vertex coordinates: A[18; 0] B[0; 0] C[1.97222222222; 5.66765985835]
Centroid: CG[6.65774074074; 1.88988661945]
Coordinates of the circumscribed circle: U[9; 0.04441181771]
Coordinates of the inscribed circle: I[3.5; 2.48877749879]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5299022748° = 160°31'44″ = 0.34398326616 rad
∠ B' = β' = 109.1990114463° = 109°11'24″ = 1.23658656456 rad
∠ C' = γ' = 90.28108627891° = 90°16'51″ = 1.56658943464 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 = 18 ; ;

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

p = a+b+c = 6+17+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-6)(20.5-17)(20.5-18) } ; ; T = sqrt{ 2600.94 } = 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 * 51 }{ 6 } = 17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51 }{ 17 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51 }{ 18 } = 5.67 ; ;

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**2-18**2 }{ 2 * 17 * 18 } ) = 19° 28'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-6**2-18**2 }{ 2 * 6 * 18 } ) = 70° 48'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-6**2-17**2 }{ 2 * 17 * 6 } ) = 89° 43'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51 }{ 20.5 } = 2.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 19° 28'16" } = 9 ; ;




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