4 23 25 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 23   c = 25

Area: T = 41.42546303544
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 8.2844336002° = 8°17'4″ = 0.14545889396 rad
Angle ∠ B = β = 55.94442022574° = 55°56'39″ = 0.97664105268 rad
Angle ∠ C = γ = 115.7711461741° = 115°46'17″ = 2.02105931872 rad

Height: ha = 20.71223151772
Height: hb = 3.60221417699
Height: hc = 3.31439704284

Median: ma = 23.93774184072
Median: mb = 13.7220422734
Median: mc = 10.78219293264

Inradius: r = 1.59332550136
Circumradius: R = 13.88106308006

Vertex coordinates: A[25; 0] B[0; 0] C[2.24; 3.31439704284]
Centroid: CG[9.08; 1.10546568095]
Coordinates of the circumscribed circle: U[12.5; -6.03550568698]
Coordinates of the inscribed circle: I[3; 1.59332550136]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.7165663998° = 171°42'56″ = 0.14545889396 rad
∠ B' = β' = 124.0565797743° = 124°3'21″ = 0.97664105268 rad
∠ C' = γ' = 64.22985382594° = 64°13'43″ = 2.02105931872 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 = 25 ; ;

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

p = a+b+c = 4+23+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-4)(26-23)(26-25) } ; ; T = sqrt{ 1716 } = 41.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.42 }{ 4 } = 20.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.42 }{ 23 } = 3.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.42 }{ 25 } = 3.31 ; ;

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**2-25**2 }{ 2 * 23 * 25 } ) = 8° 17'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-4**2-25**2 }{ 2 * 4 * 25 } ) = 55° 56'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-4**2-23**2 }{ 2 * 23 * 4 } ) = 115° 46'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.42 }{ 26 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 8° 17'4" } = 13.88 ; ;




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