12 25 26 triangle

Acute scalene triangle.

Sides: a = 12   b = 25   c = 26

Area: T = 148.1877170497
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 27.12767531173° = 27°7'36″ = 0.47334511573 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 81.0833203747° = 81°5' = 1.41551688735 rad

Height: ha = 24.69878617496
Height: hb = 11.85549736398
Height: hc = 11.39990131152

Median: ma = 24.78991105125
Median: mb = 15.93295323221
Median: mc = 14.68799182559

Inradius: r = 4.7044354619
Circumradius: R = 13.15990338992

Vertex coordinates: A[26; 0] B[0; 0] C[3.75; 11.39990131152]
Centroid: CG[9.91766666667; 3.87996710384]
Coordinates of the circumscribed circle: U[13; 2.04396502544]
Coordinates of the inscribed circle: I[6.5; 4.7044354619]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.8733246883° = 152°52'24″ = 0.47334511573 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 98.9176796253° = 98°55' = 1.41551688735 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 = 25 ; ; c = 26 ; ;

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

p = a+b+c = 12+25+26 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-12)(31.5-25)(31.5-26) } ; ; T = sqrt{ 21959.44 } = 148.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.19 }{ 12 } = 24.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.19 }{ 25 } = 11.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.19 }{ 26 } = 11.4 ; ;

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**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 27° 7'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 71° 47'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-25**2 }{ 2 * 25 * 12 } ) = 81° 5' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.19 }{ 31.5 } = 4.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 27° 7'36" } = 13.16 ; ;




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