9 17 22 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 17   c = 22

Area: T = 70.99329573972
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 22.31114770869° = 22°18'41″ = 0.38994087361 rad
Angle ∠ B = β = 45.81656148467° = 45°48'56″ = 0.87996333279 rad
Angle ∠ C = γ = 111.8732908066° = 111°52'22″ = 1.95325505895 rad

Height: ha = 15.77662127549
Height: hb = 8.3522112635
Height: hc = 6.45439052179

Median: ma = 19.1387659209
Median: mb = 14.5
Median: mc = 8

Inradius: r = 2.95880398915
Circumradius: R = 11.85332884226

Vertex coordinates: A[22; 0] B[0; 0] C[6.27327272727; 6.45439052179]
Centroid: CG[9.42442424242; 2.15113017393]
Coordinates of the circumscribed circle: U[11; -4.4165930981]
Coordinates of the inscribed circle: I[7; 2.95880398915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6898522913° = 157°41'19″ = 0.38994087361 rad
∠ B' = β' = 134.1844385153° = 134°11'4″ = 0.87996333279 rad
∠ C' = γ' = 68.12770919336° = 68°7'38″ = 1.95325505895 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 = 17 ; ; c = 22 ; ;

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

p = a+b+c = 9+17+22 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-9)(24-17)(24-22) } ; ; T = sqrt{ 5040 } = 70.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.99 }{ 9 } = 15.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.99 }{ 17 } = 8.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.99 }{ 22 } = 6.45 ; ;

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**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 22° 18'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 45° 48'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-17**2 }{ 2 * 17 * 9 } ) = 111° 52'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.99 }{ 24 } = 2.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 22° 18'41" } = 11.85 ; ;




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