18 24 29 triangle

Acute scalene triangle.

Sides: a = 18   b = 24   c = 29

Area: T = 215.4965794623
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 38.26107140477° = 38°15'39″ = 0.66877754343 rad
Angle ∠ B = β = 55.65548921569° = 55°39'18″ = 0.9711361113 rad
Angle ∠ C = γ = 86.08443937954° = 86°5'4″ = 1.50224561063 rad

Height: ha = 23.94439771803
Height: hb = 17.95879828852
Height: hc = 14.86217789395

Median: ma = 25.05499500998
Median: mb = 20.94403915914
Median: mc = 15.48438625672

Inradius: r = 6.07703040739
Circumradius: R = 14.53439263139

Vertex coordinates: A[29; 0] B[0; 0] C[10.15551724138; 14.86217789395]
Centroid: CG[13.05217241379; 4.95439263132]
Coordinates of the circumscribed circle: U[14.5; 0.99224787645]
Coordinates of the inscribed circle: I[11.5; 6.07703040739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7399285952° = 141°44'21″ = 0.66877754343 rad
∠ B' = β' = 124.3455107843° = 124°20'42″ = 0.9711361113 rad
∠ C' = γ' = 93.91656062046° = 93°54'56″ = 1.50224561063 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 = 24 ; ; c = 29 ; ;

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

p = a+b+c = 18+24+29 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-18)(35.5-24)(35.5-29) } ; ; T = sqrt{ 46438.44 } = 215.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 215.5 }{ 18 } = 23.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 215.5 }{ 24 } = 17.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 215.5 }{ 29 } = 14.86 ; ;

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**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 38° 15'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 55° 39'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-18**2-24**2 }{ 2 * 24 * 18 } ) = 86° 5'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 215.5 }{ 35.5 } = 6.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 15'39" } = 14.53 ; ;




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