7 13 14 triangle

Acute scalene triangle.

Sides: a = 7   b = 13   c = 14

Area: T = 45.16663591625
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 29.75877290681° = 29°45'28″ = 0.51993703502 rad
Angle ∠ B = β = 67.18551127773° = 67°11'6″ = 1.17326014263 rad
Angle ∠ C = γ = 83.05771581546° = 83°3'26″ = 1.45496208771 rad

Height: ha = 12.90546740464
Height: hb = 6.94986706404
Height: hc = 6.45223370232

Median: ma = 13.04879883507
Median: mb = 8.95882364336
Median: mc = 7.74659666924

Inradius: r = 2.65768446566
Circumradius: R = 7.05217085261

Vertex coordinates: A[14; 0] B[0; 0] C[2.71442857143; 6.45223370232]
Centroid: CG[5.57114285714; 2.15107790077]
Coordinates of the circumscribed circle: U[7; 0.85224043273]
Coordinates of the inscribed circle: I[4; 2.65768446566]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2422270932° = 150°14'32″ = 0.51993703502 rad
∠ B' = β' = 112.8154887223° = 112°48'54″ = 1.17326014263 rad
∠ C' = γ' = 96.94328418454° = 96°56'34″ = 1.45496208771 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 = 7 ; ; b = 13 ; ; c = 14 ; ;

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

p = a+b+c = 7+13+14 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-7)(17-13)(17-14) } ; ; T = sqrt{ 2040 } = 45.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.17 }{ 7 } = 12.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.17 }{ 13 } = 6.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.17 }{ 14 } = 6.45 ; ;

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{ 7**2-13**2-14**2 }{ 2 * 13 * 14 } ) = 29° 45'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-7**2-14**2 }{ 2 * 7 * 14 } ) = 67° 11'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-7**2-13**2 }{ 2 * 13 * 7 } ) = 83° 3'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.17 }{ 17 } = 2.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 29° 45'28" } = 7.05 ; ;




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

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