8 25 26 triangle

Acute scalene triangle.

Sides: a = 8   b = 25   c = 26

Area: T = 99.94771735468
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 17.91104255359° = 17°54'38″ = 0.3132595896 rad
Angle ∠ B = β = 73.95220152636° = 73°57'7″ = 1.29107061548 rad
Angle ∠ C = γ = 88.13875592005° = 88°8'15″ = 1.53882906027 rad

Height: ha = 24.98767933867
Height: hb = 7.99657738837
Height: hc = 7.6888244119

Median: ma = 25.18992834356
Median: mb = 14.62201915172
Median: mc = 13.24876412995

Inradius: r = 3.38880397812
Circumradius: R = 13.00768710687

Vertex coordinates: A[26; 0] B[0; 0] C[2.21215384615; 7.6888244119]
Centroid: CG[9.40438461538; 2.56327480397]
Coordinates of the circumscribed circle: U[13; 0.42327233097]
Coordinates of the inscribed circle: I[4.5; 3.38880397812]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.0989574464° = 162°5'22″ = 0.3132595896 rad
∠ B' = β' = 106.0487984736° = 106°2'53″ = 1.29107061548 rad
∠ C' = γ' = 91.86224407995° = 91°51'45″ = 1.53882906027 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 = 8 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 8+25+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-8)(29.5-25)(29.5-26) } ; ; T = sqrt{ 9989.44 } = 99.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 99.95 }{ 8 } = 24.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 99.95 }{ 25 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 99.95 }{ 26 } = 7.69 ; ;

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{ 8**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 17° 54'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-8**2-26**2 }{ 2 * 8 * 26 } ) = 73° 57'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-8**2-25**2 }{ 2 * 25 * 8 } ) = 88° 8'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 99.95 }{ 29.5 } = 3.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 17° 54'38" } = 13.01 ; ;




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