16 20 30 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 20   c = 30

Area: T = 147.9165516427
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 29.54113605001° = 29°32'29″ = 0.51655940062 rad
Angle ∠ B = β = 38.04875074536° = 38°2'51″ = 0.66440542772 rad
Angle ∠ C = γ = 112.4111132046° = 112°24'40″ = 1.96219443701 rad

Height: ha = 18.48994395534
Height: hb = 14.79215516427
Height: hc = 9.86110344285

Median: ma = 24.20774368738
Median: mb = 21.86332111091
Median: mc = 10.14988915651

Inradius: r = 4.48222883766
Circumradius: R = 16.22554782863

Vertex coordinates: A[30; 0] B[0; 0] C[12.6; 9.86110344285]
Centroid: CG[14.2; 3.28770114762]
Coordinates of the circumscribed circle: U[15; -6.18659635967]
Coordinates of the inscribed circle: I[13; 4.48222883766]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.45986395° = 150°27'31″ = 0.51655940062 rad
∠ B' = β' = 141.9522492546° = 141°57'9″ = 0.66440542772 rad
∠ C' = γ' = 67.58988679538° = 67°35'20″ = 1.96219443701 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 = 16 ; ; b = 20 ; ; c = 30 ; ;

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

p = a+b+c = 16+20+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-16)(33-20)(33-30) } ; ; T = sqrt{ 21879 } = 147.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 147.92 }{ 16 } = 18.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 147.92 }{ 20 } = 14.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 147.92 }{ 30 } = 9.86 ; ;

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{ 16**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 29° 32'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 38° 2'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 112° 24'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 147.92 }{ 33 } = 4.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 29° 32'29" } = 16.23 ; ;




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