6 22 24 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 22   c = 24

Area: T = 64.49880619864
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 14.14111102339° = 14°8'28″ = 0.24768089335 rad
Angle ∠ B = β = 63.61222000388° = 63°36'44″ = 1.11102423351 rad
Angle ∠ C = γ = 102.2476689727° = 102°14'48″ = 1.7854541385 rad

Height: ha = 21.49993539955
Height: hb = 5.86334601806
Height: hc = 5.37548384989

Median: ma = 22.8255424421
Median: mb = 13.60114705087
Median: mc = 10.77703296143

Inradius: r = 2.48106946918
Circumradius: R = 12.27994387243

Vertex coordinates: A[24; 0] B[0; 0] C[2.66766666667; 5.37548384989]
Centroid: CG[8.88988888889; 1.7921612833]
Coordinates of the circumscribed circle: U[12; -2.60547294264]
Coordinates of the inscribed circle: I[4; 2.48106946918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.8598889766° = 165°51'32″ = 0.24768089335 rad
∠ B' = β' = 116.3887799961° = 116°23'16″ = 1.11102423351 rad
∠ C' = γ' = 77.75333102727° = 77°45'12″ = 1.7854541385 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 = 6 ; ; b = 22 ; ; c = 24 ; ;

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

p = a+b+c = 6+22+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 * (26-6)(26-22)(26-24) } ; ; T = sqrt{ 4160 } = 64.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.5 }{ 6 } = 21.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.5 }{ 22 } = 5.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.5 }{ 24 } = 5.37 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 22**2+24**2-6**2 }{ 2 * 22 * 24 } ) = 14° 8'28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+24**2-22**2 }{ 2 * 6 * 24 } ) = 63° 36'44" ; ; gamma = 180° - alpha - beta = 180° - 14° 8'28" - 63° 36'44" = 102° 14'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.5 }{ 26 } = 2.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 14° 8'28" } = 12.28 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 24**2 - 6**2 } }{ 2 } = 22.825 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 6**2 - 22**2 } }{ 2 } = 13.601 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 6**2 - 24**2 } }{ 2 } = 10.77 ; ;
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