14 29 29 triangle

Acute isosceles triangle.

Sides: a = 14   b = 29   c = 29

Area: T = 196.9977461913
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 27.93659253493° = 27°56'9″ = 0.48875738769 rad
Angle ∠ B = β = 76.03220373253° = 76°1'55″ = 1.32770093883 rad
Angle ∠ C = γ = 76.03220373253° = 76°1'55″ = 1.32770093883 rad

Height: ha = 28.14224945589
Height: hb = 13.5866031856
Height: hc = 13.5866031856

Median: ma = 28.14224945589
Median: mb = 17.55770498661
Median: mc = 17.55770498661

Inradius: r = 5.47221517198
Circumradius: R = 14.94218168713

Vertex coordinates: A[29; 0] B[0; 0] C[3.37993103448; 13.5866031856]
Centroid: CG[10.79331034483; 4.52986772853]
Coordinates of the circumscribed circle: U[14.5; 3.60766454517]
Coordinates of the inscribed circle: I[7; 5.47221517198]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.0644074651° = 152°3'51″ = 0.48875738769 rad
∠ B' = β' = 103.9687962675° = 103°58'5″ = 1.32770093883 rad
∠ C' = γ' = 103.9687962675° = 103°58'5″ = 1.32770093883 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 = 14 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 14+29+29 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-14)(36-29)(36-29) } ; ; T = sqrt{ 38808 } = 197 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197 }{ 14 } = 28.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197 }{ 29 } = 13.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197 }{ 29 } = 13.59 ; ;

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{ 14**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 27° 56'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 76° 1'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-29**2 }{ 2 * 29 * 14 } ) = 76° 1'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197 }{ 36 } = 5.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 27° 56'9" } = 14.94 ; ;




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

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