7 23 23 triangle

Acute isosceles triangle.

Sides: a = 7   b = 23   c = 23

Area: T = 79.56224754517
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 17.50658581538° = 17°30'21″ = 0.30655348632 rad
Angle ∠ B = β = 81.24770709231° = 81°14'49″ = 1.41880288952 rad
Angle ∠ C = γ = 81.24770709231° = 81°14'49″ = 1.41880288952 rad

Height: ha = 22.73221358433
Height: hb = 6.91884761262
Height: hc = 6.91884761262

Median: ma = 22.73221358433
Median: mb = 12.52199840255
Median: mc = 12.52199840255

Inradius: r = 3.00223575642
Circumradius: R = 11.63655102672

Vertex coordinates: A[23; 0] B[0; 0] C[1.06552173913; 6.91884761262]
Centroid: CG[8.02217391304; 2.30661587087]
Coordinates of the circumscribed circle: U[11.5; 1.77106211276]
Coordinates of the inscribed circle: I[3.5; 3.00223575642]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.4944141846° = 162°29'39″ = 0.30655348632 rad
∠ B' = β' = 98.75329290769° = 98°45'11″ = 1.41880288952 rad
∠ C' = γ' = 98.75329290769° = 98°45'11″ = 1.41880288952 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 = 7 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 7+23+23 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-7)(26.5-23)(26.5-23) } ; ; T = sqrt{ 6330.19 } = 79.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.56 }{ 7 } = 22.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.56 }{ 23 } = 6.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.56 }{ 23 } = 6.92 ; ;

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{ 7**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 17° 30'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-7**2-23**2 }{ 2 * 7 * 23 } ) = 81° 14'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-7**2-23**2 }{ 2 * 23 * 7 } ) = 81° 14'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.56 }{ 26.5 } = 3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 17° 30'21" } = 11.64 ; ;




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