17 23 26 triangle

Acute scalene triangle.

Sides: a = 17   b = 23   c = 26

Area: T = 192.2549837451
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 40.01440953467° = 40°51″ = 0.6988377711 rad
Angle ∠ B = β = 60.44880393396° = 60°26'53″ = 1.05550173129 rad
Angle ∠ C = γ = 79.53878653137° = 79°32'16″ = 1.38881976297 rad

Height: ha = 22.61876279354
Height: hb = 16.71773771697
Height: hc = 14.78884490347

Median: ma = 23.02771578793
Median: mb = 18.71549672722
Median: mc = 15.49219333848

Inradius: r = 5.826575265
Circumradius: R = 13.22197771072

Vertex coordinates: A[26; 0] B[0; 0] C[8.38546153846; 14.78884490347]
Centroid: CG[11.46215384615; 4.92994830116]
Coordinates of the circumscribed circle: U[13; 2.40105221857]
Coordinates of the inscribed circle: I[10; 5.826575265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9865904653° = 139°59'9″ = 0.6988377711 rad
∠ B' = β' = 119.552196066° = 119°33'7″ = 1.05550173129 rad
∠ C' = γ' = 100.4622134686° = 100°27'44″ = 1.38881976297 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 17+23+26 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-17)(33-23)(33-26) } ; ; T = sqrt{ 36960 } = 192.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 192.25 }{ 17 } = 22.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 192.25 }{ 23 } = 16.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 192.25 }{ 26 } = 14.79 ; ;

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**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 40° 51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 60° 26'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 79° 32'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 192.25 }{ 33 } = 5.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 51" } = 13.22 ; ;




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