10 18 25 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 18   c = 25

Area: T = 74.66655040832
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 19.38109001271° = 19°22'51″ = 0.33882605192 rad
Angle ∠ B = β = 36.67884850469° = 36°40'43″ = 0.64401603287 rad
Angle ∠ C = γ = 123.9410614826° = 123°56'26″ = 2.16331718057 rad

Height: ha = 14.93331008166
Height: hb = 8.29661671204
Height: hc = 5.97332403267

Median: ma = 21.20114150471
Median: mb = 16.77879617356
Median: mc = 7.46765922615

Inradius: r = 2.81875661918
Circumradius: R = 15.06771988867

Vertex coordinates: A[25; 0] B[0; 0] C[8.02; 5.97332403267]
Centroid: CG[11.00766666667; 1.99110801089]
Coordinates of the circumscribed circle: U[12.5; -8.41325193784]
Coordinates of the inscribed circle: I[8.5; 2.81875661918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.6199099873° = 160°37'9″ = 0.33882605192 rad
∠ B' = β' = 143.3221514953° = 143°19'17″ = 0.64401603287 rad
∠ C' = γ' = 56.0599385174° = 56°3'34″ = 2.16331718057 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 = 10 ; ; b = 18 ; ; c = 25 ; ;

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

p = a+b+c = 10+18+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-10)(26.5-18)(26.5-25) } ; ; T = sqrt{ 5574.94 } = 74.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.67 }{ 10 } = 14.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.67 }{ 18 } = 8.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.67 }{ 25 } = 5.97 ; ;

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{ 10**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 19° 22'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 36° 40'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 123° 56'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.67 }{ 26.5 } = 2.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 19° 22'51" } = 15.07 ; ;




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