6 7 12 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 7   c = 12

Area: T = 14.94878259289
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 20.84986512302° = 20°50'55″ = 0.36438776086 rad
Angle ∠ B = β = 24.5333007117° = 24°31'59″ = 0.42881817496 rad
Angle ∠ C = γ = 134.6188341653° = 134°37'6″ = 2.35495332954 rad

Height: ha = 4.9832608643
Height: hb = 4.27108074083
Height: hc = 2.49113043215

Median: ma = 9.35441434669
Median: mb = 8.81875960443
Median: mc = 2.55495097568

Inradius: r = 1.19658260743
Circumradius: R = 8.42993194609

Vertex coordinates: A[12; 0] B[0; 0] C[5.45883333333; 2.49113043215]
Centroid: CG[5.81994444444; 0.83304347738]
Coordinates of the circumscribed circle: U[6; -5.92105934309]
Coordinates of the inscribed circle: I[5.5; 1.19658260743]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.151134877° = 159°9'5″ = 0.36438776086 rad
∠ B' = β' = 155.4676992883° = 155°28'1″ = 0.42881817496 rad
∠ C' = γ' = 45.38216583472° = 45°22'54″ = 2.35495332954 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 = 6 ; ; b = 7 ; ; c = 12 ; ;

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

p = a+b+c = 6+7+12 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-6)(12.5-7)(12.5-12) } ; ; T = sqrt{ 223.44 } = 14.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.95 }{ 6 } = 4.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.95 }{ 7 } = 4.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.95 }{ 12 } = 2.49 ; ;

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**2-7**2-12**2 }{ 2 * 7 * 12 } ) = 20° 50'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-6**2-12**2 }{ 2 * 6 * 12 } ) = 24° 31'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-6**2-7**2 }{ 2 * 7 * 6 } ) = 134° 37'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.95 }{ 12.5 } = 1.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 20° 50'55" } = 8.43 ; ;




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