23 23 27 triangle

Acute isosceles triangle.

Sides: a = 23   b = 23   c = 27

Area: T = 251.3876530069
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 54.05986701088° = 54°3'31″ = 0.94435017826 rad
Angle ∠ B = β = 54.05986701088° = 54°3'31″ = 0.94435017826 rad
Angle ∠ C = γ = 71.88326597825° = 71°52'58″ = 1.25545890883 rad

Height: ha = 21.86596982668
Height: hb = 21.86596982668
Height: hc = 18.62112244495

Median: ma = 22.2887889088
Median: mb = 22.2887889088
Median: mc = 18.62112244495

Inradius: r = 6.88773021937
Circumradius: R = 14.20442216782

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 18.62112244495]
Centroid: CG[13.5; 6.20770748165]
Coordinates of the circumscribed circle: U[13.5; 4.41770027714]
Coordinates of the inscribed circle: I[13.5; 6.88773021937]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.9411329891° = 125°56'29″ = 0.94435017826 rad
∠ B' = β' = 125.9411329891° = 125°56'29″ = 0.94435017826 rad
∠ C' = γ' = 108.1177340218° = 108°7'2″ = 1.25545890883 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 = 23 ; ; b = 23 ; ; c = 27 ; ;

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

p = a+b+c = 23+23+27 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-23)(36.5-23)(36.5-27) } ; ; T = sqrt{ 63195.19 } = 251.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 251.39 }{ 23 } = 21.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 251.39 }{ 23 } = 21.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 251.39 }{ 27 } = 18.62 ; ;

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{ 23**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 54° 3'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 54° 3'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 71° 52'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 251.39 }{ 36.5 } = 6.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 54° 3'31" } = 14.2 ; ;




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