23 25 26 triangle

Acute scalene triangle.

Sides: a = 23   b = 25   c = 26

Area: T = 261.488804944
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 53.57695793367° = 53°34'10″ = 0.93549655383 rad
Angle ∠ B = β = 60.99108143584° = 60°59'27″ = 1.0644490524 rad
Angle ∠ C = γ = 65.44396063049° = 65°26'23″ = 1.14221365912 rad

Height: ha = 22.73880912557
Height: hb = 20.91990439552
Height: hc = 20.11444653415

Median: ma = 22.76551048757
Median: mb = 21.12546301743
Median: mc = 20.19990098767

Inradius: r = 7.06772445795
Circumradius: R = 14.29331962206

Vertex coordinates: A[26; 0] B[0; 0] C[11.15438461538; 20.11444653415]
Centroid: CG[12.38546153846; 6.70548217805]
Coordinates of the circumscribed circle: U[13; 5.94109980813]
Coordinates of the inscribed circle: I[12; 7.06772445795]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.4330420663° = 126°25'50″ = 0.93549655383 rad
∠ B' = β' = 119.0099185642° = 119°33″ = 1.0644490524 rad
∠ C' = γ' = 114.5660393695° = 114°33'37″ = 1.14221365912 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 = 25 ; ; c = 26 ; ;

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

p = a+b+c = 23+25+26 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-23)(37-25)(37-26) } ; ; T = sqrt{ 68376 } = 261.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 261.49 }{ 23 } = 22.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 261.49 }{ 25 } = 20.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 261.49 }{ 26 } = 20.11 ; ;

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**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 53° 34'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 60° 59'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-23**2-25**2 }{ 2 * 25 * 23 } ) = 65° 26'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 261.49 }{ 37 } = 7.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 53° 34'10" } = 14.29 ; ;




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