3 23 23 triangle

Acute isosceles triangle.

Sides: a = 3   b = 23   c = 23

Area: T = 34.42765522526
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 7.47986704631° = 7°28'43″ = 0.13105274233 rad
Angle ∠ B = β = 86.26106647685° = 86°15'38″ = 1.50655326152 rad
Angle ∠ C = γ = 86.26106647685° = 86°15'38″ = 1.50655326152 rad

Height: ha = 22.95110348351
Height: hb = 2.99436132394
Height: hc = 2.99436132394

Median: ma = 22.95110348351
Median: mb = 11.69440155635
Median: mc = 11.69440155635

Inradius: r = 1.40551653981
Circumradius: R = 11.52545348151

Vertex coordinates: A[23; 0] B[0; 0] C[0.19656521739; 2.99436132394]
Centroid: CG[7.7321884058; 0.99878710798]
Coordinates of the circumscribed circle: U[11.5; 0.75216000966]
Coordinates of the inscribed circle: I[1.5; 1.40551653981]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.5211329537° = 172°31'17″ = 0.13105274233 rad
∠ B' = β' = 93.73993352315° = 93°44'22″ = 1.50655326152 rad
∠ C' = γ' = 93.73993352315° = 93°44'22″ = 1.50655326152 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 = 3 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 3+23+23 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-3)(24.5-23)(24.5-23) } ; ; T = sqrt{ 1185.19 } = 34.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.43 }{ 3 } = 22.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.43 }{ 23 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.43 }{ 23 } = 2.99 ; ;

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{ 3**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 7° 28'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-3**2-23**2 }{ 2 * 3 * 23 } ) = 86° 15'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-3**2-23**2 }{ 2 * 23 * 3 } ) = 86° 15'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.43 }{ 24.5 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 7° 28'43" } = 11.52 ; ;




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