16 20 29 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 20   c = 29

Area: T = 153.1769636351
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 31.88219705474° = 31°52'55″ = 0.55664453581 rad
Angle ∠ B = β = 41.31661918592° = 41°18'58″ = 0.72111035823 rad
Angle ∠ C = γ = 106.8021837593° = 106°48'7″ = 1.86440437132 rad

Height: ha = 19.14662045439
Height: hb = 15.31769636351
Height: hc = 10.56334231966

Median: ma = 23.59902522242
Median: mb = 21.17878185845
Median: mc = 10.85112672071

Inradius: r = 4.71329118877
Circumradius: R = 15.14766051318

Vertex coordinates: A[29; 0] B[0; 0] C[12.01772413793; 10.56334231966]
Centroid: CG[13.67224137931; 3.52111410655]
Coordinates of the circumscribed circle: U[14.5; -4.37883155459]
Coordinates of the inscribed circle: I[12.5; 4.71329118877]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.1188029453° = 148°7'5″ = 0.55664453581 rad
∠ B' = β' = 138.6843808141° = 138°41'2″ = 0.72111035823 rad
∠ C' = γ' = 73.19881624066° = 73°11'53″ = 1.86440437132 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 = 29 ; ;

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

p = a+b+c = 16+20+29 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-16)(32.5-20)(32.5-29) } ; ; T = sqrt{ 23460.94 } = 153.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.17 }{ 16 } = 19.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.17 }{ 20 } = 15.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.17 }{ 29 } = 10.56 ; ;

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**2-29**2 }{ 2 * 20 * 29 } ) = 31° 52'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-29**2 }{ 2 * 16 * 29 } ) = 41° 18'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 106° 48'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.17 }{ 32.5 } = 4.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 31° 52'55" } = 15.15 ; ;




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