7 18 24 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 18   c = 24

Area: T = 37.32987757635
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 9.95217277652° = 9°57'6″ = 0.17436904158 rad
Angle ∠ B = β = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ C = γ = 143.6643942485° = 143°39'50″ = 2.50774088128 rad

Height: ha = 10.66553645039
Height: hb = 4.14876417515
Height: hc = 3.11107313136

Median: ma = 20.92224759529
Median: mb = 15.21551240547
Median: mc = 6.51992024052

Inradius: r = 1.52436235006
Circumradius: R = 20.25224723765

Vertex coordinates: A[24; 0] B[0; 0] C[6.27108333333; 3.11107313136]
Centroid: CG[10.09902777778; 1.03769104379]
Coordinates of the circumscribed circle: U[12; -16.31444916367]
Coordinates of the inscribed circle: I[6.5; 1.52436235006]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.0488272235° = 170°2'54″ = 0.17436904158 rad
∠ B' = β' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ C' = γ' = 36.33660575146° = 36°20'10″ = 2.50774088128 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 = 7 ; ; b = 18 ; ; c = 24 ; ;

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

p = a+b+c = 7+18+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-7)(24.5-18)(24.5-24) } ; ; T = sqrt{ 1393.44 } = 37.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.33 }{ 7 } = 10.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.33 }{ 18 } = 4.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.33 }{ 24 } = 3.11 ; ;

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{ 7**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 9° 57'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-7**2-24**2 }{ 2 * 7 * 24 } ) = 26° 23'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-7**2-18**2 }{ 2 * 18 * 7 } ) = 143° 39'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.33 }{ 24.5 } = 1.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 9° 57'6" } = 20.25 ; ;




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