6 23 23 triangle

Acute isosceles triangle.

Sides: a = 6   b = 23   c = 23

Area: T = 68.41105255059
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 14.98994349079° = 14°59'22″ = 0.26216149922 rad
Angle ∠ B = β = 82.50552825461° = 82°30'19″ = 1.44399888307 rad
Angle ∠ C = γ = 82.50552825461° = 82°30'19″ = 1.44399888307 rad

Height: ha = 22.8043508502
Height: hb = 5.94987413483
Height: hc = 5.94987413483

Median: ma = 22.8043508502
Median: mb = 12.25876506721
Median: mc = 12.25876506721

Inradius: r = 2.63111740579
Circumradius: R = 11.59990923053

Vertex coordinates: A[23; 0] B[0; 0] C[0.78326086957; 5.94987413483]
Centroid: CG[7.92875362319; 1.98329137828]
Coordinates of the circumscribed circle: U[11.5; 1.51329250833]
Coordinates of the inscribed circle: I[3; 2.63111740579]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.0110565092° = 165°38″ = 0.26216149922 rad
∠ B' = β' = 97.49547174539° = 97°29'41″ = 1.44399888307 rad
∠ C' = γ' = 97.49547174539° = 97°29'41″ = 1.44399888307 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 = 6 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 6+23+23 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-6)(26-23)(26-23) } ; ; T = sqrt{ 4680 } = 68.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.41 }{ 6 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.41 }{ 23 } = 5.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.41 }{ 23 } = 5.95 ; ;

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{ 6**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 14° 59'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-6**2-23**2 }{ 2 * 6 * 23 } ) = 82° 30'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-6**2-23**2 }{ 2 * 23 * 6 } ) = 82° 30'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.41 }{ 26 } = 2.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 14° 59'22" } = 11.6 ; ;




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