19 25 26 triangle

Acute scalene triangle.

Sides: a = 19   b = 25   c = 26

Area: T = 224.4999443206
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 43.69108952793° = 43°41'27″ = 0.76325499758 rad
Angle ∠ B = β = 65.35444154842° = 65°21'16″ = 1.14106497309 rad
Angle ∠ C = γ = 70.95546892365° = 70°57'17″ = 1.23883929469 rad

Height: ha = 23.63215203375
Height: hb = 17.96599554565
Height: hc = 17.2699187939

Median: ma = 23.67696007571
Median: mb = 19.03328663107
Median: mc = 18

Inradius: r = 6.41442698059
Circumradius: R = 13.75328180734

Vertex coordinates: A[26; 0] B[0; 0] C[7.92330769231; 17.2699187939]
Centroid: CG[11.30876923077; 5.75663959797]
Coordinates of the circumscribed circle: U[13; 4.48877616871]
Coordinates of the inscribed circle: I[10; 6.41442698059]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.3099104721° = 136°18'33″ = 0.76325499758 rad
∠ B' = β' = 114.6465584516° = 114°38'44″ = 1.14106497309 rad
∠ C' = γ' = 109.0455310763° = 109°2'43″ = 1.23883929469 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 = 19 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 19+25+26 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-19)(35-25)(35-26) } ; ; T = sqrt{ 50400 } = 224.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 224.5 }{ 19 } = 23.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 224.5 }{ 25 } = 17.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 224.5 }{ 26 } = 17.27 ; ;

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{ 19**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 43° 41'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 65° 21'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-19**2-25**2 }{ 2 * 25 * 19 } ) = 70° 57'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 224.5 }{ 35 } = 6.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 43° 41'27" } = 13.75 ; ;




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