15 20 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 20   c = 29

Area: T = 139.9432845476
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 28.85328340448° = 28°51'10″ = 0.50435769526 rad
Angle ∠ B = β = 40.04769699311° = 40°2'49″ = 0.69989514807 rad
Angle ∠ C = γ = 111.1100196024° = 111°6'1″ = 1.93990642202 rad

Height: ha = 18.65990460635
Height: hb = 13.99442845476
Height: hc = 9.65112307225

Median: ma = 23.75439470404
Median: mb = 20.80986520467
Median: mc = 10.11218742081

Inradius: r = 4.37332139211
Circumradius: R = 15.54220592785

Vertex coordinates: A[29; 0] B[0; 0] C[11.48327586207; 9.65112307225]
Centroid: CG[13.49442528736; 3.21770769075]
Coordinates of the circumscribed circle: U[14.5; -5.59551413403]
Coordinates of the inscribed circle: I[12; 4.37332139211]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.1477165955° = 151°8'50″ = 0.50435769526 rad
∠ B' = β' = 139.9533030069° = 139°57'11″ = 0.69989514807 rad
∠ C' = γ' = 68.98998039759° = 68°53'59″ = 1.93990642202 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 = 15 ; ; b = 20 ; ; c = 29 ; ;

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

p = a+b+c = 15+20+29 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-15)(32-20)(32-29) } ; ; T = sqrt{ 19584 } = 139.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.94 }{ 15 } = 18.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.94 }{ 20 } = 13.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.94 }{ 29 } = 9.65 ; ;

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{ 15**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 28° 51'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 40° 2'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-20**2 }{ 2 * 20 * 15 } ) = 111° 6'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.94 }{ 32 } = 4.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 28° 51'10" } = 15.54 ; ;




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