14 25 26 triangle

Acute scalene triangle.

Sides: a = 14   b = 25   c = 26

Area: T = 171.2044373484
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ B = β = 70.16766380911° = 70°10' = 1.22546388597 rad
Angle ∠ C = γ = 78.04550312918° = 78°2'42″ = 1.36221427609 rad

Height: ha = 24.45877676406
Height: hb = 13.69663498787
Height: hc = 13.17695671911

Median: ma = 24.52554969369
Median: mb = 16.72657286837
Median: mc = 15.54402702679

Inradius: r = 5.26878268764
Circumradius: R = 13.28882119405

Vertex coordinates: A[26; 0] B[0; 0] C[4.75; 13.17695671911]
Centroid: CG[10.25; 4.39898557304]
Coordinates of the circumscribed circle: U[13; 2.75325581877]
Coordinates of the inscribed circle: I[7.5; 5.26878268764]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ B' = β' = 109.8333361909° = 109°50' = 1.22546388597 rad
∠ C' = γ' = 101.9554968708° = 101°57'18″ = 1.36221427609 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 = 14 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 14+25+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-14)(32.5-25)(32.5-26) } ; ; T = sqrt{ 29310.94 } = 171.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.2 }{ 14 } = 24.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.2 }{ 25 } = 13.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.2 }{ 26 } = 13.17 ; ;

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{ 14**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 31° 47'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 70° 10' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-25**2 }{ 2 * 25 * 14 } ) = 78° 2'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.2 }{ 32.5 } = 5.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 47'18" } = 13.29 ; ;




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