14 14 24 triangle

Obtuse isosceles triangle.

Sides: a = 14   b = 14   c = 24

Area: T = 86.53332306111
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 31.00327191339° = 31°10″ = 0.5411099526 rad
Angle ∠ B = β = 31.00327191339° = 31°10″ = 0.5411099526 rad
Angle ∠ C = γ = 117.9954561732° = 117°59'40″ = 2.05993936017 rad

Height: ha = 12.36218900873
Height: hb = 12.36218900873
Height: hc = 7.21111025509

Median: ma = 18.35875597507
Median: mb = 18.35875597507
Median: mc = 7.21111025509

Inradius: r = 3.32882011774
Circumradius: R = 13.59901548075

Vertex coordinates: A[24; 0] B[0; 0] C[12; 7.21111025509]
Centroid: CG[12; 2.40437008503]
Coordinates of the circumscribed circle: U[12; -6.37990522566]
Coordinates of the inscribed circle: I[12; 3.32882011774]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.9977280866° = 148°59'50″ = 0.5411099526 rad
∠ B' = β' = 148.9977280866° = 148°59'50″ = 0.5411099526 rad
∠ C' = γ' = 62.00554382677° = 62°20″ = 2.05993936017 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 = 14 ; ; c = 24 ; ;

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

p = a+b+c = 14+14+24 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-14)(26-14)(26-24) } ; ; T = sqrt{ 7488 } = 86.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.53 }{ 14 } = 12.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.53 }{ 14 } = 12.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.53 }{ 24 } = 7.21 ; ;

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**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 31° 10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 31° 10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 117° 59'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.53 }{ 26 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 10" } = 13.59 ; ;




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

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