16 20 24 triangle

Acute scalene triangle.

Sides: a = 16   b = 20   c = 24

Area: T = 158.7455078664
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 55.77111336722° = 55°46'16″ = 0.97333899101 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 19.8433134833
Height: hb = 15.87545078664
Height: hc = 13.22987565553

Median: ma = 20.5911260282
Median: mb = 17.77663888346
Median: mc = 13.56546599663

Inradius: r = 5.29215026221
Circumradius: R = 12.09548631363

Vertex coordinates: A[24; 0] B[0; 0] C[9; 13.22987565553]
Centroid: CG[11; 4.41095855184]
Coordinates of the circumscribed circle: U[12; 1.5121857892]
Coordinates of the inscribed circle: I[10; 5.29215026221]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 124.2298866328° = 124°13'44″ = 0.97333899101 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 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 = 16 ; ; b = 20 ; ; c = 24 ; ;

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

p = a+b+c = 16+20+24 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-16)(30-20)(30-24) } ; ; T = sqrt{ 25200 } = 158.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 158.75 }{ 16 } = 19.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 158.75 }{ 20 } = 15.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 158.75 }{ 24 } = 13.23 ; ;

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{ 16**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 41° 24'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 55° 46'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 82° 49'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 158.75 }{ 30 } = 5.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 41° 24'35" } = 12.09 ; ;




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