3 29 30 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 29   c = 30

Area: T = 41.6655333312
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 5.49663519766° = 5°29'47″ = 0.09659294388 rad
Angle ∠ B = β = 67.80438991432° = 67°48'14″ = 1.18334012857 rad
Angle ∠ C = γ = 106.769974888° = 106°41'59″ = 1.8622261929 rad

Height: ha = 27.77768888747
Height: hb = 2.87334712629
Height: hc = 2.77876888875

Median: ma = 29.46660821963
Median: mb = 15.62884996081
Median: mc = 14.14221356237

Inradius: r = 1.34440430101
Circumradius: R = 15.66105011441

Vertex coordinates: A[30; 0] B[0; 0] C[1.13333333333; 2.77876888875]
Centroid: CG[10.37877777778; 0.92658962958]
Coordinates of the circumscribed circle: U[15; -4.55001440069]
Coordinates of the inscribed circle: I[2; 1.34440430101]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.5043648023° = 174°30'13″ = 0.09659294388 rad
∠ B' = β' = 112.1966100857° = 112°11'46″ = 1.18334012857 rad
∠ C' = γ' = 73.33002511197° = 73°18'1″ = 1.8622261929 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 3+29+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-3)(31-29)(31-30) } ; ; T = sqrt{ 1736 } = 41.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.67 }{ 3 } = 27.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.67 }{ 29 } = 2.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.67 }{ 30 } = 2.78 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 5° 29'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-3**2-30**2 }{ 2 * 3 * 30 } ) = 67° 48'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-3**2-29**2 }{ 2 * 29 * 3 } ) = 106° 41'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.67 }{ 31 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 29'47" } = 15.66 ; ;




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