23 24 26 triangle

Acute scalene triangle.

Sides: a = 23   b = 24   c = 26

Area: T = 254.3109727498
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 54.59767840917° = 54°35'48″ = 0.95328936434 rad
Angle ∠ B = β = 58.27698201529° = 58°16'11″ = 1.01770002162 rad
Angle ∠ C = γ = 67.13333957554° = 67°8' = 1.1721698794 rad

Height: ha = 22.11438893476
Height: hb = 21.19224772915
Height: hc = 19.56222867306

Median: ma = 22.22204860433
Median: mb = 21.41326131054
Median: mc = 19.58331560276

Inradius: r = 6.96773897945
Circumradius: R = 14.10987800113

Vertex coordinates: A[26; 0] B[0; 0] C[12.09661538462; 19.56222867306]
Centroid: CG[12.69987179487; 6.52107622435]
Coordinates of the circumscribed circle: U[13; 5.48224878848]
Coordinates of the inscribed circle: I[12.5; 6.96773897945]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.4033215908° = 125°24'12″ = 0.95328936434 rad
∠ B' = β' = 121.7330179847° = 121°43'49″ = 1.01770002162 rad
∠ C' = γ' = 112.8676604245° = 112°52' = 1.1721698794 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 = 23 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 23+24+26 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-23)(36.5-24)(36.5-26) } ; ; T = sqrt{ 64673.44 } = 254.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 254.31 }{ 23 } = 22.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 254.31 }{ 24 } = 21.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 254.31 }{ 26 } = 19.56 ; ;

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{ 23**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 54° 35'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 58° 16'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-23**2-24**2 }{ 2 * 24 * 23 } ) = 67° 8' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 254.31 }{ 36.5 } = 6.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 54° 35'48" } = 14.11 ; ;




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