23 25 28 triangle

Acute scalene triangle.

Sides: a = 23   b = 25   c = 28

Area: T = 272.2133151776
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 51.05551964059° = 51°3'19″ = 0.89110812775 rad
Angle ∠ B = β = 57.7132936368° = 57°42'47″ = 1.00772807606 rad
Angle ∠ C = γ = 71.23218672261° = 71°13'55″ = 1.24332306154 rad

Height: ha = 23.67107088501
Height: hb = 21.77770521421
Height: hc = 19.44437965555

Median: ma = 23.92217474278
Median: mb = 22.36662692463
Median: mc = 19.51992212959

Inradius: r = 7.16435039941
Circumradius: R = 14.78662069622

Vertex coordinates: A[28; 0] B[0; 0] C[12.28657142857; 19.44437965555]
Centroid: CG[13.42985714286; 6.48112655185]
Coordinates of the circumscribed circle: U[14; 4.75773013704]
Coordinates of the inscribed circle: I[13; 7.16435039941]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.9454803594° = 128°56'41″ = 0.89110812775 rad
∠ B' = β' = 122.2877063632° = 122°17'13″ = 1.00772807606 rad
∠ C' = γ' = 108.7688132774° = 108°46'5″ = 1.24332306154 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 23+25+28 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-23)(38-25)(38-28) } ; ; T = sqrt{ 74100 } = 272.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 272.21 }{ 23 } = 23.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 272.21 }{ 25 } = 21.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 272.21 }{ 28 } = 19.44 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 51° 3'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 57° 42'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-23**2-25**2 }{ 2 * 25 * 23 } ) = 71° 13'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 272.21 }{ 38 } = 7.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 51° 3'19" } = 14.79 ; ;




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