3 27 29 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 27   c = 29

Area: T = 31.26599984005
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 4.58797563582° = 4°34'47″ = 0.08799318274 rad
Angle ∠ B = β = 45.9410716098° = 45°56'27″ = 0.80218167566 rad
Angle ∠ C = γ = 129.4879527544° = 129°28'46″ = 2.26598440696 rad

Height: ha = 20.84399989337
Height: hb = 2.31655554371
Height: hc = 2.15658619587

Median: ma = 27.97876696671
Median: mb = 15.58804364509
Median: mc = 12.65996031684

Inradius: r = 1.06596609627
Circumradius: R = 18.78659894449

Vertex coordinates: A[29; 0] B[0; 0] C[2.08662068966; 2.15658619587]
Centroid: CG[10.36220689655; 0.71986206529]
Coordinates of the circumscribed circle: U[14.5; -11.94441784742]
Coordinates of the inscribed circle: I[2.5; 1.06596609627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.4220243642° = 175°25'13″ = 0.08799318274 rad
∠ B' = β' = 134.0599283902° = 134°3'33″ = 0.80218167566 rad
∠ C' = γ' = 50.52204724562° = 50°31'14″ = 2.26598440696 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 = 3 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 3+27+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-3)(29.5-27)(29.5-29) } ; ; T = sqrt{ 977.19 } = 31.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.26 }{ 3 } = 20.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.26 }{ 27 } = 2.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.26 }{ 29 } = 2.16 ; ;

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{ 3**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 4° 34'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-3**2-29**2 }{ 2 * 3 * 29 } ) = 45° 56'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-3**2-27**2 }{ 2 * 27 * 3 } ) = 129° 28'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.26 }{ 29.5 } = 1.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 4° 34'47" } = 18.79 ; ;




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