13 18 24 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 18   c = 24

Area: T = 115.1455288657
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 32.21437979172° = 32°12'50″ = 0.56222368382 rad
Angle ∠ B = β = 47.57107345118° = 47°34'15″ = 0.83302659448 rad
Angle ∠ C = γ = 100.2155467571° = 100°12'56″ = 1.74990898705 rad

Height: ha = 17.71546597934
Height: hb = 12.79439209619
Height: hc = 9.59554407215

Median: ma = 20.19328205063
Median: mb = 17.0733371079
Median: mc = 10.12442283657

Inradius: r = 4.18771014057
Circumradius: R = 12.19332908968

Vertex coordinates: A[24; 0] B[0; 0] C[8.77108333333; 9.59554407215]
Centroid: CG[10.92436111111; 3.19884802405]
Coordinates of the circumscribed circle: U[12; -2.16224853514]
Coordinates of the inscribed circle: I[9.5; 4.18771014057]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7866202083° = 147°47'10″ = 0.56222368382 rad
∠ B' = β' = 132.4299265488° = 132°25'45″ = 0.83302659448 rad
∠ C' = γ' = 79.7854532429° = 79°47'4″ = 1.74990898705 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 = 13 ; ; b = 18 ; ; c = 24 ; ;

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

p = a+b+c = 13+18+24 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-13)(27.5-18)(27.5-24) } ; ; T = sqrt{ 13258.44 } = 115.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.15 }{ 13 } = 17.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.15 }{ 18 } = 12.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.15 }{ 24 } = 9.6 ; ;

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{ 13**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 32° 12'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-24**2 }{ 2 * 13 * 24 } ) = 47° 34'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 100° 12'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.15 }{ 27.5 } = 4.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 32° 12'50" } = 12.19 ; ;




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