8 22 24 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 22   c = 24

Area: T = 87.72111491033
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 19.40770433824° = 19°24'25″ = 0.33987168051 rad
Angle ∠ B = β = 66.03105176822° = 66°1'50″ = 1.15224499404 rad
Angle ∠ C = γ = 94.56224389353° = 94°33'45″ = 1.65504259081 rad

Height: ha = 21.93302872758
Height: hb = 7.97546499185
Height: hc = 7.31100957586

Median: ma = 22.67215680975
Median: mb = 14.10767359797
Median: mc = 11.4021754251

Inradius: r = 3.24989314483
Circumradius: R = 12.03881459978

Vertex coordinates: A[24; 0] B[0; 0] C[3.25; 7.31100957586]
Centroid: CG[9.08333333333; 2.43766985862]
Coordinates of the circumscribed circle: U[12; -0.95875797953]
Coordinates of the inscribed circle: I[5; 3.24989314483]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5932956618° = 160°35'35″ = 0.33987168051 rad
∠ B' = β' = 113.9699482318° = 113°58'10″ = 1.15224499404 rad
∠ C' = γ' = 85.43875610647° = 85°26'15″ = 1.65504259081 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 = 8 ; ; b = 22 ; ; c = 24 ; ;

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

p = a+b+c = 8+22+24 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-8)(27-22)(27-24) } ; ; T = sqrt{ 7695 } = 87.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87.72 }{ 8 } = 21.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87.72 }{ 22 } = 7.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87.72 }{ 24 } = 7.31 ; ;

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{ 8**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 19° 24'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-8**2-24**2 }{ 2 * 8 * 24 } ) = 66° 1'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-8**2-22**2 }{ 2 * 22 * 8 } ) = 94° 33'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87.72 }{ 27 } = 3.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 19° 24'25" } = 12.04 ; ;




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