14 17 18 triangle

Acute scalene triangle.

Sides: a = 14   b = 17   c = 18

Area: T = 111.986632729
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 47.04990078078° = 47°2'56″ = 0.8211160096 rad
Angle ∠ B = β = 62.7220387264° = 62°43'13″ = 1.09546772659 rad
Angle ∠ C = γ = 70.23106049282° = 70°13'50″ = 1.22657552917 rad

Height: ha = 15.99880467558
Height: hb = 13.17548620342
Height: hc = 12.44329252545

Median: ma = 16.04768065359
Median: mb = 13.7022189606
Median: mc = 12.70882650271

Inradius: r = 4.57108705017
Circumradius: R = 9.56436675111

Vertex coordinates: A[18; 0] B[0; 0] C[6.41766666667; 12.44329252545]
Centroid: CG[8.13988888889; 4.14876417515]
Coordinates of the circumscribed circle: U[9; 3.23547698935]
Coordinates of the inscribed circle: I[7.5; 4.57108705017]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.9510992192° = 132°57'4″ = 0.8211160096 rad
∠ B' = β' = 117.2879612736° = 117°16'47″ = 1.09546772659 rad
∠ C' = γ' = 109.7699395072° = 109°46'10″ = 1.22657552917 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 = 14 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 14+17+18 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-14)(24.5-17)(24.5-18) } ; ; T = sqrt{ 12540.94 } = 111.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 111.99 }{ 14 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 111.99 }{ 17 } = 13.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 111.99 }{ 18 } = 12.44 ; ;

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{ 14**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 47° 2'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 62° 43'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 70° 13'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 111.99 }{ 24.5 } = 4.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 47° 2'56" } = 9.56 ; ;




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