17 17 23 triangle

Acute isosceles triangle.

Sides: a = 17   b = 17   c = 23

Area: T = 143.9879816294
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 47.43215457967° = 47°25'54″ = 0.82878366435 rad
Angle ∠ B = β = 47.43215457967° = 47°25'54″ = 0.82878366435 rad
Angle ∠ C = γ = 85.13769084066° = 85°8'13″ = 1.48659193667 rad

Height: ha = 16.93988019169
Height: hb = 16.93988019169
Height: hc = 12.52199840255

Median: ma = 18.35107493035
Median: mb = 18.35107493035
Median: mc = 12.52199840255

Inradius: r = 5.05219233787
Circumradius: R = 11.54215482724

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 12.52199840255]
Centroid: CG[11.5; 4.17333280085]
Coordinates of the circumscribed circle: U[11.5; 0.97884357532]
Coordinates of the inscribed circle: I[11.5; 5.05219233787]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.5688454203° = 132°34'6″ = 0.82878366435 rad
∠ B' = β' = 132.5688454203° = 132°34'6″ = 0.82878366435 rad
∠ C' = γ' = 94.86330915934° = 94°51'47″ = 1.48659193667 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 = 17 ; ; c = 23 ; ;

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

p = a+b+c = 17+17+23 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-17)(28.5-17)(28.5-23) } ; ; T = sqrt{ 20730.19 } = 143.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 143.98 }{ 17 } = 16.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 143.98 }{ 17 } = 16.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 143.98 }{ 23 } = 12.52 ; ;

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**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 47° 25'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 47° 25'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 85° 8'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 143.98 }{ 28.5 } = 5.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 47° 25'54" } = 11.54 ; ;




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