18 22 29 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 22   c = 29

Area: T = 197.8288050337
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 38.32771349636° = 38°19'38″ = 0.6698934698 rad
Angle ∠ B = β = 49.28548495732° = 49°17'5″ = 0.86601828964 rad
Angle ∠ C = γ = 92.38880154633° = 92°23'17″ = 1.61224750592 rad

Height: ha = 21.98108944819
Height: hb = 17.98443682124
Height: hc = 13.64333138163

Median: ma = 24.11443111036
Median: mb = 21.48325510589
Median: mc = 13.91994109071

Inradius: r = 5.73441463866
Circumradius: R = 14.51326032184

Vertex coordinates: A[29; 0] B[0; 0] C[11.74113793103; 13.64333138163]
Centroid: CG[13.58804597701; 4.54877712721]
Coordinates of the circumscribed circle: U[14.5; -0.60546918008]
Coordinates of the inscribed circle: I[12.5; 5.73441463866]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.6732865036° = 141°40'22″ = 0.6698934698 rad
∠ B' = β' = 130.7155150427° = 130°42'55″ = 0.86601828964 rad
∠ C' = γ' = 87.61219845367° = 87°36'43″ = 1.61224750592 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 = 18 ; ; b = 22 ; ; c = 29 ; ;

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

p = a+b+c = 18+22+29 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-18)(34.5-22)(34.5-29) } ; ; T = sqrt{ 39135.94 } = 197.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.83 }{ 18 } = 21.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.83 }{ 22 } = 17.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.83 }{ 29 } = 13.64 ; ;

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{ 18**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 38° 19'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 49° 17'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-18**2-22**2 }{ 2 * 22 * 18 } ) = 92° 23'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.83 }{ 34.5 } = 5.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 19'38" } = 14.51 ; ;




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