13 18 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 18   c = 25

Area: T = 112.2549721603
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ B = β = 43.69108952793° = 43°41'27″ = 0.76325499758 rad
Angle ∠ C = γ = 106.3832669854° = 106°22'58″ = 1.8576727856 rad

Height: ha = 17.2699187939
Height: hb = 12.47221912892
Height: hc = 8.98799777283

Median: ma = 20.79106228863
Median: mb = 17.77663888346
Median: mc = 9.5

Inradius: r = 4.00989186287
Circumradius: R = 13.02989855432

Vertex coordinates: A[25; 0] B[0; 0] C[9.4; 8.98799777283]
Centroid: CG[11.46766666667; 2.99333259094]
Coordinates of the circumscribed circle: U[12.5; -3.67548420763]
Coordinates of the inscribed circle: I[10; 4.00989186287]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ B' = β' = 136.3099104721° = 136°18'33″ = 0.76325499758 rad
∠ C' = γ' = 73.61773301459° = 73°37'2″ = 1.8576727856 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 = 13 ; ; b = 18 ; ; c = 25 ; ;

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

p = a+b+c = 13+18+25 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-13)(28-18)(28-25) } ; ; T = sqrt{ 12600 } = 112.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.25 }{ 13 } = 17.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.25 }{ 18 } = 12.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.25 }{ 25 } = 8.98 ; ;

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{ 13**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 29° 55'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 43° 41'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 106° 22'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.25 }{ 28 } = 4.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 29° 55'35" } = 13.03 ; ;




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