7 14 20 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 14   c = 20

Area: T = 29.99106235347
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 12.37696965171° = 12°22'11″ = 0.21658919317 rad
Angle ∠ B = β = 25.36884394418° = 25°22'6″ = 0.44327627944 rad
Angle ∠ C = γ = 142.2621864041° = 142°15'43″ = 2.48329379275 rad

Height: ha = 8.56987495813
Height: hb = 4.28443747907
Height: hc = 2.99990623535

Median: ma = 16.90441415044
Median: mb = 13.24876412995
Median: mc = 4.74334164903

Inradius: r = 1.46329572456
Circumradius: R = 16.33884398938

Vertex coordinates: A[20; 0] B[0; 0] C[6.325; 2.99990623535]
Centroid: CG[8.775; 10.9996874512]
Coordinates of the circumscribed circle: U[10; -12.92107050181]
Coordinates of the inscribed circle: I[6.5; 1.46329572456]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6330303483° = 167°37'49″ = 0.21658919317 rad
∠ B' = β' = 154.6321560558° = 154°37'54″ = 0.44327627944 rad
∠ C' = γ' = 37.73881359589° = 37°44'17″ = 2.48329379275 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 = 14 ; ; c = 20 ; ;

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

p = a+b+c = 7+14+20 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-7)(20.5-14)(20.5-20) } ; ; T = sqrt{ 899.44 } = 29.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.99 }{ 7 } = 8.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.99 }{ 14 } = 4.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.99 }{ 20 } = 3 ; ;

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**2-14**2-20**2 }{ 2 * 14 * 20 } ) = 12° 22'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-20**2 }{ 2 * 7 * 20 } ) = 25° 22'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 142° 15'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.99 }{ 20.5 } = 1.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 12° 22'11" } = 16.34 ; ;




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

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