11 18 25 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 18   c = 25

Area: T = 88.18216307402
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 39.8990390145° = 39°53'25″ = 0.69662186479 rad
Angle ∠ C = γ = 117.0365691789° = 117°2'8″ = 2.04326581641 rad

Height: ha = 16.03330237709
Height: hb = 9.79879589711
Height: hc = 7.05545304592

Median: ma = 21.07772389084
Median: mb = 17.08880074906
Median: mc = 8.1399410298

Inradius: r = 3.26659863237
Circumradius: R = 14.03435349847

Vertex coordinates: A[25; 0] B[0; 0] C[8.44; 7.05545304592]
Centroid: CG[11.14766666667; 2.35215101531]
Coordinates of the circumscribed circle: U[12.5; -6.37988795385]
Coordinates of the inscribed circle: I[9; 3.26659863237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 140.1109609855° = 140°6'35″ = 0.69662186479 rad
∠ C' = γ' = 62.96443082106° = 62°57'52″ = 2.04326581641 rad

Calculate another triangle




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 = 11 ; ; b = 18 ; ; c = 25 ; ;

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

p = a+b+c = 11+18+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-11)(27-18)(27-25) } ; ; T = sqrt{ 7776 } = 88.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.18 }{ 11 } = 16.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.18 }{ 18 } = 9.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.18 }{ 25 } = 7.05 ; ;

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{ 11**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 23° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 39° 53'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 117° 2'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.18 }{ 27 } = 3.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 4'26" } = 14.03 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.