6 6 7 triangle

Acute isosceles triangle.

Sides: a = 6   b = 6   c = 7

Area: T = 17.05768901034
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 71.37106694253° = 71°22'14″ = 1.24656531708 rad

Height: ha = 5.68656300345
Height: hb = 5.68656300345
Height: hc = 4.87333971724

Median: ma = 5.78879184514
Median: mb = 5.78879184514
Median: mc = 4.87333971724

Inradius: r = 1.79554621161
Circumradius: R = 3.69435220675

Vertex coordinates: A[7; 0] B[0; 0] C[3.5; 4.87333971724]
Centroid: CG[3.5; 1.62444657241]
Coordinates of the circumscribed circle: U[3.5; 1.18798751049]
Coordinates of the inscribed circle: I[3.5; 1.79554621161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 108.6299330575° = 108°37'46″ = 1.24656531708 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 = 6 ; ; c = 7 ; ;

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

p = a+b+c = 6+6+7 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-6)(9.5-6)(9.5-7) } ; ; T = sqrt{ 290.94 } = 17.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.06 }{ 6 } = 5.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.06 }{ 6 } = 5.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.06 }{ 7 } = 4.87 ; ;

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**2-6**2-7**2 }{ 2 * 6 * 7 } ) = 54° 18'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-6**2-7**2 }{ 2 * 6 * 7 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-6**2-6**2 }{ 2 * 6 * 6 } ) = 71° 22'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.06 }{ 9.5 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 54° 18'53" } = 3.69 ; ;




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