4 13 14 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 13   c = 14

Area: T = 25.85441582729
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 16.50657537272° = 16°30'21″ = 0.28880797481 rad
Angle ∠ B = β = 67.42327592381° = 67°25'22″ = 1.17767491395 rad
Angle ∠ C = γ = 96.07114870347° = 96°4'17″ = 1.6776763766 rad

Height: ha = 12.92770791364
Height: hb = 3.97875628112
Height: hc = 3.69334511818

Median: ma = 13.36603892159
Median: mb = 7.98443597113
Median: mc = 6.59554529791

Inradius: r = 1.66880102112
Circumradius: R = 7.03994865723

Vertex coordinates: A[14; 0] B[0; 0] C[1.53657142857; 3.69334511818]
Centroid: CG[5.17985714286; 1.23111503939]
Coordinates of the circumscribed circle: U[7; -0.74545610798]
Coordinates of the inscribed circle: I[2.5; 1.66880102112]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.4944246273° = 163°29'39″ = 0.28880797481 rad
∠ B' = β' = 112.5777240762° = 112°34'38″ = 1.17767491395 rad
∠ C' = γ' = 83.92985129653° = 83°55'43″ = 1.6776763766 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 = 4 ; ; b = 13 ; ; c = 14 ; ;

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

p = a+b+c = 4+13+14 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-4)(15.5-13)(15.5-14) } ; ; T = sqrt{ 668.44 } = 25.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.85 }{ 4 } = 12.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.85 }{ 13 } = 3.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.85 }{ 14 } = 3.69 ; ;

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{ 4**2-13**2-14**2 }{ 2 * 13 * 14 } ) = 16° 30'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-4**2-14**2 }{ 2 * 4 * 14 } ) = 67° 25'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-4**2-13**2 }{ 2 * 13 * 4 } ) = 96° 4'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.85 }{ 15.5 } = 1.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 16° 30'21" } = 7.04 ; ;




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

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