4 28 29 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 28   c = 29

Area: T = 55.05439508119
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 7.79333663715° = 7°47'36″ = 0.1366019903 rad
Angle ∠ B = β = 71.66600018715° = 71°39'36″ = 1.25107029746 rad
Angle ∠ C = γ = 100.5476631757° = 100°32'48″ = 1.75548697759 rad

Height: ha = 27.5276975406
Height: hb = 3.9322425058
Height: hc = 3.79768241939

Median: ma = 28.43441344162
Median: mb = 15.2487950682
Median: mc = 13.7754977314

Inradius: r = 1.80550475676
Circumradius: R = 14.74991685524

Vertex coordinates: A[29; 0] B[0; 0] C[1.25986206897; 3.79768241939]
Centroid: CG[10.08662068966; 1.26656080646]
Coordinates of the circumscribed circle: U[14.5; -2.76996246011]
Coordinates of the inscribed circle: I[2.5; 1.80550475676]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.2076633629° = 172°12'24″ = 0.1366019903 rad
∠ B' = β' = 108.3439998128° = 108°20'24″ = 1.25107029746 rad
∠ C' = γ' = 79.4533368243° = 79°27'12″ = 1.75548697759 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 = 4 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 4+28+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-4)(30.5-28)(30.5-29) } ; ; T = sqrt{ 3030.94 } = 55.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.05 }{ 4 } = 27.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.05 }{ 28 } = 3.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.05 }{ 29 } = 3.8 ; ;

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{ 4**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 7° 47'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-4**2-29**2 }{ 2 * 4 * 29 } ) = 71° 39'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-4**2-28**2 }{ 2 * 28 * 4 } ) = 100° 32'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.05 }{ 30.5 } = 1.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 47'36" } = 14.75 ; ;




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