19 24 28 triangle

Acute scalene triangle.

Sides: a = 19   b = 24   c = 28

Area: T = 224.7698631041
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 41.98664052375° = 41°59'11″ = 0.73328010125 rad
Angle ∠ B = β = 57.67113844812° = 57°40'17″ = 1.00765555434 rad
Angle ∠ C = γ = 80.34222102813° = 80°20'32″ = 1.40222360977 rad

Height: ha = 23.6659855899
Height: hb = 18.73107192534
Height: hc = 16.05549022172

Median: ma = 24.28547688892
Median: mb = 20.77002415445
Median: mc = 16.50875740192

Inradius: r = 6.33215107335
Circumradius: R = 14.20112699246

Vertex coordinates: A[28; 0] B[0; 0] C[10.16107142857; 16.05549022172]
Centroid: CG[12.72202380952; 5.35216340724]
Coordinates of the circumscribed circle: U[14; 2.38224498887]
Coordinates of the inscribed circle: I[11.5; 6.33215107335]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0143594762° = 138°49″ = 0.73328010125 rad
∠ B' = β' = 122.3298615519° = 122°19'43″ = 1.00765555434 rad
∠ C' = γ' = 99.65877897187° = 99°39'28″ = 1.40222360977 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 = 19 ; ; b = 24 ; ; c = 28 ; ;

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

p = a+b+c = 19+24+28 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-19)(35.5-24)(35.5-28) } ; ; T = sqrt{ 50520.94 } = 224.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 224.77 }{ 19 } = 23.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 224.77 }{ 24 } = 18.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 224.77 }{ 28 } = 16.05 ; ;

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{ 19**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 41° 59'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 57° 40'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-19**2-24**2 }{ 2 * 24 * 19 } ) = 80° 20'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 224.77 }{ 35.5 } = 6.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 41° 59'11" } = 14.2 ; ;




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