10 25 26 triangle

Acute scalene triangle.

Sides: a = 10   b = 25   c = 26

Area: T = 124.3988301837
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 22.5054996964° = 22°30'18″ = 0.39327862952 rad
Angle ∠ B = β = 73.11990162165° = 73°7'8″ = 1.27661675788 rad
Angle ∠ C = γ = 84.37659868195° = 84°22'34″ = 1.47326387796 rad

Height: ha = 24.88796603675
Height: hb = 9.9521864147
Height: hc = 9.56991001413

Median: ma = 25.01099980008
Median: mb = 15.22333373476
Median: mc = 13.91104277432

Inradius: r = 4.07986328471
Circumradius: R = 13.06328792837

Vertex coordinates: A[26; 0] B[0; 0] C[2.90438461538; 9.56991001413]
Centroid: CG[9.63546153846; 3.19897000471]
Coordinates of the circumscribed circle: U[13; 1.28801621698]
Coordinates of the inscribed circle: I[5.5; 4.07986328471]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.4955003036° = 157°29'42″ = 0.39327862952 rad
∠ B' = β' = 106.8810983783° = 106°52'52″ = 1.27661675788 rad
∠ C' = γ' = 95.62440131805° = 95°37'26″ = 1.47326387796 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 = 10 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 10+25+26 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-10)(30.5-25)(30.5-26) } ; ; T = sqrt{ 15474.94 } = 124.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.4 }{ 10 } = 24.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.4 }{ 25 } = 9.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.4 }{ 26 } = 9.57 ; ;

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{ 10**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 22° 30'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 73° 7'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-25**2 }{ 2 * 25 * 10 } ) = 84° 22'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.4 }{ 30.5 } = 4.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 30'18" } = 13.06 ; ;




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