15 19 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 19   c = 29

Area: T = 127.445484101
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 27.55546661768° = 27°33'17″ = 0.48109196491 rad
Angle ∠ B = β = 35.87703643042° = 35°52'13″ = 0.6266055961 rad
Angle ∠ C = γ = 116.5754969519° = 116°34'30″ = 2.03546170435 rad

Height: ha = 16.9932645468
Height: hb = 13.41552464221
Height: hc = 8.789929938

Median: ma = 23.3439880034
Median: mb = 21.04216254125
Median: mc = 9.09767026993

Inradius: r = 4.04658679686
Circumradius: R = 16.21328963686

Vertex coordinates: A[29; 0] B[0; 0] C[12.15551724138; 8.789929938]
Centroid: CG[13.71883908046; 2.932976646]
Coordinates of the circumscribed circle: U[14.5; -7.25331378491]
Coordinates of the inscribed circle: I[12.5; 4.04658679686]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.4455333823° = 152°26'43″ = 0.48109196491 rad
∠ B' = β' = 144.1329635696° = 144°7'47″ = 0.6266055961 rad
∠ C' = γ' = 63.4255030481° = 63°25'30″ = 2.03546170435 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 = 19 ; ; c = 29 ; ;

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

p = a+b+c = 15+19+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-15)(31.5-19)(31.5-29) } ; ; T = sqrt{ 16242.19 } = 127.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.44 }{ 15 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.44 }{ 19 } = 13.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.44 }{ 29 } = 8.79 ; ;

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**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 27° 33'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 35° 52'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-19**2 }{ 2 * 19 * 15 } ) = 116° 34'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.44 }{ 31.5 } = 4.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 27° 33'17" } = 16.21 ; ;




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