3 28 30 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 28   c = 30

Area: T = 32.38795846175
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 4.42215624392° = 4°25'18″ = 0.07771708226 rad
Angle ∠ B = β = 46.01770368696° = 46°1'1″ = 0.80331488054 rad
Angle ∠ C = γ = 129.5611400691° = 129°33'41″ = 2.26112730256 rad

Height: ha = 21.5866389745
Height: hb = 2.31328274727
Height: hc = 2.15986389745

Median: ma = 28.97884402617
Median: mb = 16.07879351908
Median: mc = 13.09658008537

Inradius: r = 1.06216257252
Circumradius: R = 19.45767041994

Vertex coordinates: A[30; 0] B[0; 0] C[2.08333333333; 2.15986389745]
Centroid: CG[10.69444444444; 0.72195463248]
Coordinates of the circumscribed circle: U[15; -12.39220675555]
Coordinates of the inscribed circle: I[2.5; 1.06216257252]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5788437561° = 175°34'42″ = 0.07771708226 rad
∠ B' = β' = 133.983296313° = 133°58'59″ = 0.80331488054 rad
∠ C' = γ' = 50.43985993088° = 50°26'19″ = 2.26112730256 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 = 28 ; ; c = 30 ; ;

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

p = a+b+c = 3+28+30 = 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 * (30.5-3)(30.5-28)(30.5-30) } ; ; T = sqrt{ 1048.44 } = 32.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.38 }{ 3 } = 21.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.38 }{ 28 } = 2.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.38 }{ 30 } = 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**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 4° 25'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-3**2-30**2 }{ 2 * 3 * 30 } ) = 46° 1'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-3**2-28**2 }{ 2 * 28 * 3 } ) = 129° 33'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.38 }{ 30.5 } = 1.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 4° 25'18" } = 19.46 ; ;




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