5 20 24 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 20   c = 24

Area: T = 32.78662394916
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 7.85216900217° = 7°51'6″ = 0.13770378427 rad
Angle ∠ B = β = 33.12329402077° = 33°7'23″ = 0.57881043646 rad
Angle ∠ C = γ = 139.0255369771° = 139°1'31″ = 2.42664504463 rad

Height: ha = 13.11444957966
Height: hb = 3.27986239492
Height: hc = 2.73221866243

Median: ma = 21.94988040676
Median: mb = 14.16598022585
Median: mc = 8.27664726786

Inradius: r = 1.33882138568
Circumradius: R = 18.33003604349

Vertex coordinates: A[24; 0] B[0; 0] C[4.18875; 2.73221866243]
Centroid: CG[9.39658333333; 0.91107288748]
Coordinates of the circumscribed circle: U[12; -13.81767721283]
Coordinates of the inscribed circle: I[4.5; 1.33882138568]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.1488309978° = 172°8'54″ = 0.13770378427 rad
∠ B' = β' = 146.8777059792° = 146°52'37″ = 0.57881043646 rad
∠ C' = γ' = 40.97546302294° = 40°58'29″ = 2.42664504463 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 = 5 ; ; b = 20 ; ; c = 24 ; ;

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

p = a+b+c = 5+20+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 * (24.5-5)(24.5-20)(24.5-24) } ; ; T = sqrt{ 1074.94 } = 32.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.79 }{ 5 } = 13.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.79 }{ 20 } = 3.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.79 }{ 24 } = 2.73 ; ;

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{ 5**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 7° 51'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-5**2-24**2 }{ 2 * 5 * 24 } ) = 33° 7'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-5**2-20**2 }{ 2 * 20 * 5 } ) = 139° 1'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.79 }{ 24.5 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 7° 51'6" } = 18.3 ; ;




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