17 25 26 triangle

Acute scalene triangle.

Sides: a = 17   b = 25   c = 26

Area: T = 204
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 38.88800696564° = 38°52'48″ = 0.67985852289 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 73.74397952917° = 73°44'23″ = 1.28770022176 rad

Height: ha = 24
Height: hb = 16.32
Height: hc = 15.69223076923

Median: ma = 24.04768293128
Median: mb = 18.06223918682
Median: mc = 16.97105627485

Inradius: r = 6
Circumradius: R = 13.54216666667

Vertex coordinates: A[26; 0] B[0; 0] C[6.53884615385; 15.69223076923]
Centroid: CG[10.84661538462; 5.23107692308]
Coordinates of the circumscribed circle: U[13; 3.79216666667]
Coordinates of the inscribed circle: I[9; 6]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.1219930344° = 141°7'12″ = 0.67985852289 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 106.2660204708° = 106°15'37″ = 1.28770022176 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 = 17 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 17+25+26 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-17)(34-25)(34-26) } ; ; T = sqrt{ 41616 } = 204 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 204 }{ 17 } = 24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 204 }{ 25 } = 16.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 204 }{ 26 } = 15.69 ; ;

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{ 17**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 38° 52'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-25**2 }{ 2 * 25 * 17 } ) = 73° 44'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 204 }{ 34 } = 6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 38° 52'48" } = 13.54 ; ;




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