5 14 16 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 14   c = 16

Area: T = 33.88986042793
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 17.61224390704° = 17°36'45″ = 0.30773950511 rad
Angle ∠ B = β = 57.91100487437° = 57°54'36″ = 1.01107210206 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 13.55554417117
Height: hb = 4.84112291828
Height: hc = 4.23660755349

Median: ma = 14.82439670804
Median: mb = 9.56655632349
Median: mc = 6.81990908485

Inradius: r = 1.93664916731
Circumradius: R = 8.26223644719

Vertex coordinates: A[16; 0] B[0; 0] C[2.656625; 4.23660755349]
Centroid: CG[6.219875; 1.41220251783]
Coordinates of the circumscribed circle: U[8; -2.0665591118]
Coordinates of the inscribed circle: I[3.5; 1.93664916731]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.388756093° = 162°23'15″ = 0.30773950511 rad
∠ B' = β' = 122.0989951256° = 122°5'24″ = 1.01107210206 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 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 = 5 ; ; b = 14 ; ; c = 16 ; ;

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

p = a+b+c = 5+14+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-5)(17.5-14)(17.5-16) } ; ; T = sqrt{ 1148.44 } = 33.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.89 }{ 5 } = 13.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.89 }{ 14 } = 4.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.89 }{ 16 } = 4.24 ; ;

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{ 5**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 17° 36'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-5**2-16**2 }{ 2 * 5 * 16 } ) = 57° 54'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-5**2-14**2 }{ 2 * 14 * 5 } ) = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.89 }{ 17.5 } = 1.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 17° 36'45" } = 8.26 ; ;




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

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