4 23 23 triangle

Acute isosceles triangle.

Sides: a = 4   b = 23   c = 23

Area: T = 45.82657569496
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 9.97770839511° = 9°58'37″ = 0.17441329647 rad
Angle ∠ B = β = 85.01114580244° = 85°41″ = 1.48437298444 rad
Angle ∠ C = γ = 85.01114580244° = 85°41″ = 1.48437298444 rad

Height: ha = 22.91328784748
Height: hb = 3.98548484304
Height: hc = 3.98548484304

Median: ma = 22.91328784748
Median: mb = 11.84327192823
Median: mc = 11.84327192823

Inradius: r = 1.8333030278
Circumradius: R = 11.54437263935

Vertex coordinates: A[23; 0] B[0; 0] C[0.3487826087; 3.98548484304]
Centroid: CG[7.78326086957; 1.32882828101]
Coordinates of the circumscribed circle: U[11.5; 1.00438022951]
Coordinates of the inscribed circle: I[2; 1.8333030278]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.0232916049° = 170°1'23″ = 0.17441329647 rad
∠ B' = β' = 94.98985419756° = 94°59'19″ = 1.48437298444 rad
∠ C' = γ' = 94.98985419756° = 94°59'19″ = 1.48437298444 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 = 4 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 4+23+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-4)(25-23)(25-23) } ; ; T = sqrt{ 2100 } = 45.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.83 }{ 4 } = 22.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.83 }{ 23 } = 3.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.83 }{ 23 } = 3.98 ; ;

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{ 4**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 9° 58'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-4**2-23**2 }{ 2 * 4 * 23 } ) = 85° 41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-4**2-23**2 }{ 2 * 23 * 4 } ) = 85° 41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.83 }{ 25 } = 1.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 58'37" } = 11.54 ; ;




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