9 14 22 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 14   c = 22

Area: T = 35.9329618701
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 13.49219775635° = 13°29'31″ = 0.23554794311 rad
Angle ∠ B = β = 21.28799664684° = 21°16'48″ = 0.37114054796 rad
Angle ∠ C = γ = 145.2288055968° = 145°13'41″ = 2.53547077429 rad

Height: ha = 7.98443597113
Height: hb = 5.13328026716
Height: hc = 3.26663289728

Median: ma = 17.88215547422
Median: mb = 15.28107067899
Median: mc = 4.18333001327

Inradius: r = 1.59768719423
Circumradius: R = 19.28877081654

Vertex coordinates: A[22; 0] B[0; 0] C[8.38663636364; 3.26663289728]
Centroid: CG[10.12987878788; 1.08987763243]
Coordinates of the circumscribed circle: U[11; -15.84334745645]
Coordinates of the inscribed circle: I[8.5; 1.59768719423]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.5088022436° = 166°30'29″ = 0.23554794311 rad
∠ B' = β' = 158.7220033532° = 158°43'12″ = 0.37114054796 rad
∠ C' = γ' = 34.77219440319° = 34°46'19″ = 2.53547077429 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 = 9 ; ; b = 14 ; ; c = 22 ; ;

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

p = a+b+c = 9+14+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 * (22.5-9)(22.5-14)(22.5-22) } ; ; T = sqrt{ 1290.94 } = 35.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.93 }{ 9 } = 7.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.93 }{ 14 } = 5.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.93 }{ 22 } = 3.27 ; ;

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{ 9**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 13° 29'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 21° 16'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-14**2 }{ 2 * 14 * 9 } ) = 145° 13'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.93 }{ 22.5 } = 1.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 13° 29'31" } = 19.29 ; ;




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