1 23 23 triangle

Acute isosceles triangle.

Sides: a = 1   b = 23   c = 23

Area: T = 11.49772822876
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 2.49113171032° = 2°29'29″ = 0.04334816862 rad
Angle ∠ B = β = 88.75443414484° = 88°45'16″ = 1.54990554837 rad
Angle ∠ C = γ = 88.75443414484° = 88°45'16″ = 1.54990554837 rad

Height: ha = 22.99545645751
Height: hb = 10.9997636772
Height: hc = 10.9997636772

Median: ma = 22.99545645751
Median: mb = 11.52217186218
Median: mc = 11.52217186218

Inradius: r = 0.48992460548
Circumradius: R = 11.50327183548

Vertex coordinates: A[23; 0] B[0; 0] C[0.02217391304; 10.9997636772]
Centroid: CG[7.67439130435; 0.33332545591]
Coordinates of the circumscribed circle: U[11.5; 0.25500590947]
Coordinates of the inscribed circle: I[0.5; 0.48992460548]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.5098682897° = 177°30'31″ = 0.04334816862 rad
∠ B' = β' = 91.24656585516° = 91°14'44″ = 1.54990554837 rad
∠ C' = γ' = 91.24656585516° = 91°14'44″ = 1.54990554837 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 = 1 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 1+23+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-1)(23.5-23)(23.5-23) } ; ; T = sqrt{ 132.19 } = 11.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.5 }{ 1 } = 22.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.5 }{ 23 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.5 }{ 23 } = 1 ; ;

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{ 1**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 2° 29'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-1**2-23**2 }{ 2 * 1 * 23 } ) = 88° 45'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-1**2-23**2 }{ 2 * 23 * 1 } ) = 88° 45'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.5 }{ 23.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 29'29" } = 11.5 ; ;




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