13 15 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 15   c = 25

Area: T = 78.55769061254
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 24.77695868266° = 24°46'11″ = 0.43223108445 rad
Angle ∠ B = β = 28.90994725423° = 28°54'34″ = 0.50545654809 rad
Angle ∠ C = γ = 126.3210940631° = 126°19'15″ = 2.20547163282 rad

Height: ha = 12.08656778655
Height: hb = 10.47442541501
Height: hc = 6.285455249

Median: ma = 19.56439975465
Median: mb = 18.4599414942
Median: mc = 6.38435726674

Inradius: r = 2.96444115519
Circumradius: R = 15.51442311493

Vertex coordinates: A[25; 0] B[0; 0] C[11.38; 6.285455249]
Centroid: CG[12.12766666667; 2.095485083]
Coordinates of the circumscribed circle: U[12.5; -9.18991984499]
Coordinates of the inscribed circle: I[11.5; 2.96444115519]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.2330413173° = 155°13'49″ = 0.43223108445 rad
∠ B' = β' = 151.0910527458° = 151°5'26″ = 0.50545654809 rad
∠ C' = γ' = 53.67990593689° = 53°40'45″ = 2.20547163282 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 = 15 ; ; c = 25 ; ;

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

p = a+b+c = 13+15+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 * (26.5-13)(26.5-15)(26.5-25) } ; ; T = sqrt{ 6171.19 } = 78.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.56 }{ 13 } = 12.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.56 }{ 15 } = 10.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.56 }{ 25 } = 6.28 ; ;

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**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 24° 46'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 28° 54'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-15**2 }{ 2 * 15 * 13 } ) = 126° 19'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.56 }{ 26.5 } = 2.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 24° 46'11" } = 15.51 ; ;




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