18 25 29 triangle

Acute scalene triangle.

Sides: a = 18   b = 25   c = 29

Area: T = 223.3744125628
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 38.03994925009° = 38°2'22″ = 0.66439143899 rad
Angle ∠ B = β = 58.85326100785° = 58°51'9″ = 1.02771718193 rad
Angle ∠ C = γ = 83.10878974207° = 83°6'28″ = 1.45105064444 rad

Height: ha = 24.8199347292
Height: hb = 17.87699300502
Height: hc = 15.40551121123

Median: ma = 25.53442906696
Median: mb = 20.64658228221
Median: mc = 16.2565768207

Inradius: r = 6.2054836823
Circumradius: R = 14.6065541223

Vertex coordinates: A[29; 0] B[0; 0] C[9.31103448276; 15.40551121123]
Centroid: CG[12.77701149425; 5.13550373708]
Coordinates of the circumscribed circle: U[14.5; 1.75326649468]
Coordinates of the inscribed circle: I[11; 6.2054836823]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.9610507499° = 141°57'38″ = 0.66439143899 rad
∠ B' = β' = 121.1477389922° = 121°8'51″ = 1.02771718193 rad
∠ C' = γ' = 96.89221025793° = 96°53'32″ = 1.45105064444 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 18+25+29 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-18)(36-25)(36-29) } ; ; T = sqrt{ 49896 } = 223.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 223.37 }{ 18 } = 24.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 223.37 }{ 25 } = 17.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 223.37 }{ 29 } = 15.41 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 38° 2'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 58° 51'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-18**2-25**2 }{ 2 * 25 * 18 } ) = 83° 6'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 223.37 }{ 36 } = 6.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 2'22" } = 14.61 ; ;




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