6 25 29 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 25   c = 29

Area: T = 60
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 9.52772833815° = 9°31'38″ = 0.16662824638 rad
Angle ∠ B = β = 43.60328189727° = 43°36'10″ = 0.76110127542 rad
Angle ∠ C = γ = 126.8769897646° = 126°52'12″ = 2.21442974356 rad

Height: ha = 20
Height: hb = 4.8
Height: hc = 4.13879310345

Median: ma = 26.90772480941
Median: mb = 16.88002976164
Median: mc = 10.96658560997

Inradius: r = 2
Circumradius: R = 18.125

Vertex coordinates: A[29; 0] B[0; 0] C[4.34548275862; 4.13879310345]
Centroid: CG[11.11549425287; 1.37993103448]
Coordinates of the circumscribed circle: U[14.5; -10.875]
Coordinates of the inscribed circle: I[5; 2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.4732716619° = 170°28'22″ = 0.16662824638 rad
∠ B' = β' = 136.3977181027° = 136°23'50″ = 0.76110127542 rad
∠ C' = γ' = 53.13301023542° = 53°7'48″ = 2.21442974356 rad

Calculate another triangle




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 = 6 ; ; b = 25 ; ; c = 29 ; ;

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

p = a+b+c = 6+25+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-6)(30-25)(30-29) } ; ; T = sqrt{ 3600 } = 60 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60 }{ 6 } = 20 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60 }{ 25 } = 4.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60 }{ 29 } = 4.14 ; ;

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{ 6**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 9° 31'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-6**2-29**2 }{ 2 * 6 * 29 } ) = 43° 36'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-6**2-25**2 }{ 2 * 25 * 6 } ) = 126° 52'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60 }{ 30 } = 2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 9° 31'38" } = 18.13 ; ;




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