8 14 21 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 14   c = 21

Area: T = 32.99114761719
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 12.96994688473° = 12°58'10″ = 0.22663599336 rad
Angle ∠ B = β = 23.12660741872° = 23°7'34″ = 0.40436261376 rad
Angle ∠ C = γ = 143.9044456966° = 143°54'16″ = 2.51216065823 rad

Height: ha = 8.2487869043
Height: hb = 4.71330680246
Height: hc = 3.14220453497

Median: ma = 17.39325271309
Median: mb = 14.26553426177
Median: mc = 4.44440972087

Inradius: r = 1.53444872638
Circumradius: R = 17.82327854048

Vertex coordinates: A[21; 0] B[0; 0] C[7.35771428571; 3.14220453497]
Centroid: CG[9.45223809524; 1.04773484499]
Coordinates of the circumscribed circle: U[10.5; -14.40114471352]
Coordinates of the inscribed circle: I[7.5; 1.53444872638]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.0310531153° = 167°1'50″ = 0.22663599336 rad
∠ B' = β' = 156.8743925813° = 156°52'26″ = 0.40436261376 rad
∠ C' = γ' = 36.09655430345° = 36°5'44″ = 2.51216065823 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 = 8 ; ; b = 14 ; ; c = 21 ; ;

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

p = a+b+c = 8+14+21 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-8)(21.5-14)(21.5-21) } ; ; T = sqrt{ 1088.44 } = 32.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.99 }{ 8 } = 8.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.99 }{ 14 } = 4.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.99 }{ 21 } = 3.14 ; ;

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{ 8**2-14**2-21**2 }{ 2 * 14 * 21 } ) = 12° 58'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-8**2-21**2 }{ 2 * 8 * 21 } ) = 23° 7'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-8**2-14**2 }{ 2 * 14 * 8 } ) = 143° 54'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.99 }{ 21.5 } = 1.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 12° 58'10" } = 17.82 ; ;




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

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