5 23 23 triangle

Acute isosceles triangle.

Sides: a = 5   b = 23   c = 23

Area: T = 57.15993168259
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 12.48802621965° = 12°28'49″ = 0.21878216668 rad
Angle ∠ B = β = 83.76598689017° = 83°45'36″ = 1.46218854934 rad
Angle ∠ C = γ = 83.76598689017° = 83°45'36″ = 1.46218854934 rad

Height: ha = 22.86437267303
Height: hb = 4.97703753762
Height: hc = 4.97703753762

Median: ma = 22.86437267303
Median: mb = 12.03112094155
Median: mc = 12.03112094155

Inradius: r = 2.24215418363
Circumradius: R = 11.56985427454

Vertex coordinates: A[23; 0] B[0; 0] C[0.54334782609; 4.97703753762]
Centroid: CG[7.8487826087; 1.65767917921]
Coordinates of the circumscribed circle: U[11.5; 1.25774502984]
Coordinates of the inscribed circle: I[2.5; 2.24215418363]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.5219737803° = 167°31'11″ = 0.21878216668 rad
∠ B' = β' = 96.24401310983° = 96°14'24″ = 1.46218854934 rad
∠ C' = γ' = 96.24401310983° = 96°14'24″ = 1.46218854934 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 = 5 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 5+23+23 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-5)(25.5-23)(25.5-23) } ; ; T = sqrt{ 3267.19 } = 57.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.16 }{ 5 } = 22.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.16 }{ 23 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.16 }{ 23 } = 4.97 ; ;

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{ 5**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 12° 28'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-5**2-23**2 }{ 2 * 5 * 23 } ) = 83° 45'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-5**2-23**2 }{ 2 * 23 * 5 } ) = 83° 45'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.16 }{ 25.5 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 12° 28'49" } = 11.57 ; ;




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