7 28 29 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 28   c = 29

Area: T = 97.98795897113
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 13.96549945758° = 13°57'54″ = 0.24437351354 rad
Angle ∠ B = β = 74.86656226185° = 74°51'56″ = 1.30766516112 rad
Angle ∠ C = γ = 91.16993828056° = 91°10'10″ = 1.5911205907 rad

Height: ha = 27.9944168489
Height: hb = 6.99985421222
Height: hc = 6.75772130835

Median: ma = 28.28986903196
Median: mb = 15.78797338381
Median: mc = 14.36114066163

Inradius: r = 3.06218621785
Circumradius: R = 14.50330205187

Vertex coordinates: A[29; 0] B[0; 0] C[1.82875862069; 6.75772130835]
Centroid: CG[10.2765862069; 2.25224043612]
Coordinates of the circumscribed circle: U[14.5; -0.29659800106]
Coordinates of the inscribed circle: I[4; 3.06218621785]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0355005424° = 166°2'6″ = 0.24437351354 rad
∠ B' = β' = 105.1344377381° = 105°8'4″ = 1.30766516112 rad
∠ C' = γ' = 88.83106171944° = 88°49'50″ = 1.5911205907 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 = 28 ; ; c = 29 ; ;

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

p = a+b+c = 7+28+29 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-7)(32-28)(32-29) } ; ; T = sqrt{ 9600 } = 97.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.98 }{ 7 } = 27.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.98 }{ 28 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.98 }{ 29 } = 6.76 ; ;

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**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 13° 57'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 74° 51'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-28**2 }{ 2 * 28 * 7 } ) = 91° 10'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.98 }{ 32 } = 3.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 57'54" } = 14.5 ; ;




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

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