14 17 22 triangle

Acute scalene triangle.

Sides: a = 14   b = 17   c = 22

Area: T = 1198.999737395
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 39.52110920523° = 39°31'16″ = 0.69897731803 rad
Angle ∠ B = β = 50.59992773209° = 50°35'57″ = 0.88331239884 rad
Angle ∠ C = γ = 89.88796306268° = 89°52'47″ = 1.56986954849 rad

Height: ha = 176.999962485
Height: hb = 143.9999691053
Height: hc = 10.8188157945

Median: ma = 18.37111730709
Median: mb = 16.3633068172
Median: mc = 11.02327038425

Inradius: r = 4.49105561281
Circumradius: R = 111.0000242745

Vertex coordinates: A[22; 0] B[0; 0] C[8.88663636364; 10.8188157945]
Centroid: CG[10.29554545455; 3.60660526483]
Coordinates of the circumscribed circle: U[11; 0.02331092947]
Coordinates of the inscribed circle: I[9.5; 4.49105561281]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.4798907948° = 140°28'44″ = 0.69897731803 rad
∠ B' = β' = 129.4010722679° = 129°24'3″ = 0.88331239884 rad
∠ C' = γ' = 90.12203693732° = 90°7'13″ = 1.56986954849 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 = 22 ; ;

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

p = a+b+c = 14+17+22 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-14)(26.5-17)(26.5-22) } ; ; T = sqrt{ 14160.94 } = 119 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119 }{ 14 } = 17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119 }{ 17 } = 14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119 }{ 22 } = 10.82 ; ;

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**2-22**2 }{ 2 * 17 * 22 } ) = 39° 31'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 50° 35'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 89° 52'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119 }{ 26.5 } = 4.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 39° 31'16" } = 11 ; ;




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