12 23 25 triangle

Acute scalene triangle.

Sides: a = 12   b = 23   c = 25

Area: T = 137.4777270849
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 28.56767204538° = 28°34' = 0.49985833284 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 85.01114580244° = 85°41″ = 1.48437298444 rad

Height: ha = 22.91328784748
Height: hb = 11.95545452912
Height: hc = 10.99881816679

Median: ma = 23.25994066992
Median: mb = 15.88223801743
Median: mc = 13.42657215821

Inradius: r = 4.5832575695
Circumradius: R = 12.54875286886

Vertex coordinates: A[25; 0] B[0; 0] C[4.8; 10.99881816679]
Centroid: CG[9.93333333333; 3.6666060556]
Coordinates of the circumscribed circle: U[12.5; 1.09110894512]
Coordinates of the inscribed circle: I[7; 4.5832575695]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.4333279546° = 151°26' = 0.49985833284 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 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 = 12 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 12+23+25 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-12)(30-23)(30-25) } ; ; T = sqrt{ 18900 } = 137.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.48 }{ 12 } = 22.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.48 }{ 23 } = 11.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.48 }{ 25 } = 11 ; ;

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{ 12**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 28° 34' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 66° 25'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-23**2 }{ 2 * 23 * 12 } ) = 85° 41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.48 }{ 30 } = 4.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 28° 34' } = 12.55 ; ;




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