20 25 29 triangle

Acute scalene triangle.

Sides: a = 20   b = 25   c = 29

Area: T = 245.7321560855
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 42.67882131475° = 42°40'42″ = 0.74548753383 rad
Angle ∠ B = β = 57.92546226621° = 57°55'29″ = 1.01109753834 rad
Angle ∠ C = γ = 79.39771641904° = 79°23'50″ = 1.38657419319 rad

Height: ha = 24.57331560855
Height: hb = 19.65985248684
Height: hc = 16.94770041969

Median: ma = 25.15994912508
Median: mb = 21.54664614264
Median: mc = 17.38553386507

Inradius: r = 6.64113935366
Circumradius: R = 14.75218698347

Vertex coordinates: A[29; 0] B[0; 0] C[10.62106896552; 16.94770041969]
Centroid: CG[13.20768965517; 5.6499001399]
Coordinates of the circumscribed circle: U[14.5; 2.71443440496]
Coordinates of the inscribed circle: I[12; 6.64113935366]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.3221786852° = 137°19'18″ = 0.74548753383 rad
∠ B' = β' = 122.0755377338° = 122°4'31″ = 1.01109753834 rad
∠ C' = γ' = 100.603283581° = 100°36'10″ = 1.38657419319 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 = 20 ; ; b = 25 ; ; c = 29 ; ;

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

p = a+b+c = 20+25+29 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-20)(37-25)(37-29) } ; ; T = sqrt{ 60384 } = 245.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 245.73 }{ 20 } = 24.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 245.73 }{ 25 } = 19.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 245.73 }{ 29 } = 16.95 ; ;

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{ 20**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 42° 40'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 57° 55'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-20**2-25**2 }{ 2 * 25 * 20 } ) = 79° 23'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 245.73 }{ 37 } = 6.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 42° 40'42" } = 14.75 ; ;




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