6 8 8 triangle

Acute isosceles triangle.

Sides: a = 6   b = 8   c = 8

Area: T = 22.24985954613
Perimeter: p = 22
Semiperimeter: s = 11

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 67.9765687163° = 67°58'32″ = 1.18663995523 rad

Height: ha = 7.41661984871
Height: hb = 5.56221488653
Height: hc = 5.56221488653

Median: ma = 7.41661984871
Median: mb = 5.83109518948
Median: mc = 5.83109518948

Inradius: r = 2.02325995874
Circumradius: R = 4.31548791198

Vertex coordinates: A[8; 0] B[0; 0] C[2.25; 5.56221488653]
Centroid: CG[3.41766666667; 1.85440496218]
Coordinates of the circumscribed circle: U[4; 1.61880796699]
Coordinates of the inscribed circle: I[3; 2.02325995874]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 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 = 8 ; ; c = 8 ; ;

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

p = a+b+c = 6+8+8 = 22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22 }{ 2 } = 11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11 * (11-6)(11-8)(11-8) } ; ; T = sqrt{ 495 } = 22.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.25 }{ 6 } = 7.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.25 }{ 8 } = 5.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.25 }{ 8 } = 5.56 ; ;

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**2-8**2-8**2 }{ 2 * 8 * 8 } ) = 44° 2'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-6**2-8**2 }{ 2 * 6 * 8 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-6**2-8**2 }{ 2 * 8 * 6 } ) = 67° 58'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.25 }{ 11 } = 2.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 44° 2'55" } = 4.31 ; ;




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