6 7 10 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 7   c = 10

Area: T = 20.66224659709
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 36.18222872212° = 36°10'56″ = 0.63215000429 rad
Angle ∠ B = β = 43.53111521674° = 43°31'52″ = 0.76597619325 rad
Angle ∠ C = γ = 100.2876560611° = 100°17'12″ = 1.75503306782 rad

Height: ha = 6.8877488657
Height: hb = 5.9043561706
Height: hc = 4.13224931942

Median: ma = 8.09332070281
Median: mb = 7.46765922615
Median: mc = 4.18333001327

Inradius: r = 1.79767361714
Circumradius: R = 5.08216780605

Vertex coordinates: A[10; 0] B[0; 0] C[4.35; 4.13224931942]
Centroid: CG[4.78333333333; 1.37774977314]
Coordinates of the circumscribed circle: U[5; -0.90774425108]
Coordinates of the inscribed circle: I[4.5; 1.79767361714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.8187712779° = 143°49'4″ = 0.63215000429 rad
∠ B' = β' = 136.4698847833° = 136°28'8″ = 0.76597619325 rad
∠ C' = γ' = 79.71334393885° = 79°42'48″ = 1.75503306782 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 = 10 ; ;

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

p = a+b+c = 6+7+10 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-6)(11.5-7)(11.5-10) } ; ; T = sqrt{ 426.94 } = 20.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.66 }{ 6 } = 6.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.66 }{ 7 } = 5.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.66 }{ 10 } = 4.13 ; ;

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**2-10**2 }{ 2 * 7 * 10 } ) = 36° 10'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-6**2-10**2 }{ 2 * 6 * 10 } ) = 43° 31'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-6**2-7**2 }{ 2 * 7 * 6 } ) = 100° 17'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.66 }{ 11.5 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 36° 10'56" } = 5.08 ; ;




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