10 18 24 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 18   c = 24

Area: T = 81.58443122175
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 22.19216065663° = 22°11'30″ = 0.38773166009 rad
Angle ∠ B = β = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ C = γ = 114.9754965368° = 114°58'30″ = 2.0076691703 rad

Height: ha = 16.31768624435
Height: hb = 9.06549235797
Height: hc = 6.79986926848

Median: ma = 20.61655281281
Median: mb = 16.03112195419
Median: mc = 8.24662112512

Inradius: r = 3.13878581622
Circumradius: R = 13.23878391218

Vertex coordinates: A[24; 0] B[0; 0] C[7.33333333333; 6.79986926848]
Centroid: CG[10.44444444444; 2.26662308949]
Coordinates of the circumscribed circle: U[12; -5.58993098514]
Coordinates of the inscribed circle: I[8; 3.13878581622]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8088393434° = 157°48'30″ = 0.38773166009 rad
∠ B' = β' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ C' = γ' = 65.02550346323° = 65°1'30″ = 2.0076691703 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 = 10 ; ; b = 18 ; ; c = 24 ; ;

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

p = a+b+c = 10+18+24 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-10)(26-18)(26-24) } ; ; T = sqrt{ 6656 } = 81.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.58 }{ 10 } = 16.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.58 }{ 18 } = 9.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.58 }{ 24 } = 6.8 ; ;

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{ 10**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 22° 11'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-24**2 }{ 2 * 10 * 24 } ) = 42° 50' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 114° 58'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.58 }{ 26 } = 3.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 11'30" } = 13.24 ; ;




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