24 26 28 triangle

Acute scalene triangle.

Sides: a = 24   b = 26   c = 28

Area: T = 289.2321740997
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 52.61768015821° = 52°37' = 0.91883364295 rad
Angle ∠ B = β = 59.40875112549° = 59°24'27″ = 1.03768566718 rad
Angle ∠ C = γ = 67.9765687163° = 67°58'32″ = 1.18663995523 rad

Height: ha = 24.10326450831
Height: hb = 22.24985954613
Height: hc = 20.65994100712

Median: ma = 24.20774368738
Median: mb = 22.60553091109
Median: mc = 20.73664413533

Inradius: r = 7.41661984871
Circumradius: R = 15.10220769192

Vertex coordinates: A[28; 0] B[0; 0] C[12.21442857143; 20.65994100712]
Centroid: CG[13.40547619048; 6.88664700237]
Coordinates of the circumscribed circle: U[14; 5.66332788447]
Coordinates of the inscribed circle: I[13; 7.41661984871]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.3833198418° = 127°23' = 0.91883364295 rad
∠ B' = β' = 120.5922488745° = 120°35'33″ = 1.03768566718 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 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 = 24 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 24+26+28 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-24)(39-26)(39-28) } ; ; T = sqrt{ 83655 } = 289.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 289.23 }{ 24 } = 24.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 289.23 }{ 26 } = 22.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 289.23 }{ 28 } = 20.66 ; ;

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{ 24**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 52° 37' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 59° 24'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-24**2-26**2 }{ 2 * 26 * 24 } ) = 67° 58'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 289.23 }{ 39 } = 7.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 52° 37' } = 15.1 ; ;




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