17 21 26 triangle

Acute scalene triangle.

Sides: a = 17   b = 21   c = 26

Area: T = 177.989876369
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 40.69105605975° = 40°41'26″ = 0.71101842569 rad
Angle ∠ B = β = 53.64768753478° = 53°38'49″ = 0.93663146082 rad
Angle ∠ C = γ = 85.66325640547° = 85°39'45″ = 1.49550937885 rad

Height: ha = 20.94398545518
Height: hb = 16.95113108276
Height: hc = 13.69114433608

Median: ma = 22.05110770712
Median: mb = 19.29437813816
Median: mc = 14

Inradius: r = 5.56221488653
Circumradius: R = 13.03773398404

Vertex coordinates: A[26; 0] B[0; 0] C[10.07769230769; 13.69114433608]
Centroid: CG[12.02656410256; 4.56438144536]
Coordinates of the circumscribed circle: U[13; 0.98660172989]
Coordinates of the inscribed circle: I[11; 5.56221488653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.3099439402° = 139°18'34″ = 0.71101842569 rad
∠ B' = β' = 126.3533124652° = 126°21'11″ = 0.93663146082 rad
∠ C' = γ' = 94.33774359453° = 94°20'15″ = 1.49550937885 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 = 21 ; ; c = 26 ; ;

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

p = a+b+c = 17+21+26 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-21)(32-26) } ; ; T = sqrt{ 31680 } = 177.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 177.99 }{ 17 } = 20.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 177.99 }{ 21 } = 16.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 177.99 }{ 26 } = 13.69 ; ;

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**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 40° 41'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 53° 38'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-21**2 }{ 2 * 21 * 17 } ) = 85° 39'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 177.99 }{ 32 } = 5.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 41'26" } = 13.04 ; ;




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