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

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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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 28**2+29**2-7**2 }{ 2 * 28 * 29 } ) = 13° 57'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+29**2-28**2 }{ 2 * 7 * 29 } ) = 74° 51'56" ; ; gamma = 180° - alpha - beta = 180° - 13° 57'54" - 74° 51'56" = 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 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 29**2 - 7**2 } }{ 2 } = 28.289 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 7**2 - 28**2 } }{ 2 } = 15.78 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 7**2 - 29**2 } }{ 2 } = 14.361 ; ;
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