1 6 6 triangle

Acute isosceles triangle.

Sides: a = 1   b = 6   c = 6

Area: T = 2.99895651858
Perimeter: p = 13
Semiperimeter: s = 6.5

Angle ∠ A = α = 9.56603836944° = 9°33'37″ = 0.16768601732 rad
Angle ∠ B = β = 85.22198081528° = 85°13'11″ = 1.48773662402 rad
Angle ∠ C = γ = 85.22198081528° = 85°13'11″ = 1.48773662402 rad

Height: ha = 5.97991303716
Height: hb = 0.99765217286
Height: hc = 0.99765217286

Median: ma = 5.97991303716
Median: mb = 3.08222070015
Median: mc = 3.08222070015

Inradius: r = 0.46599331055
Circumradius: R = 3.0110471236

Vertex coordinates: A[6; 0] B[0; 0] C[0.08333333333; 0.99765217286]
Centroid: CG[2.02877777778; 0.33221739095]
Coordinates of the circumscribed circle: U[3; 0.2510872603]
Coordinates of the inscribed circle: I[0.5; 0.46599331055]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.4439616306° = 170°26'23″ = 0.16768601732 rad
∠ B' = β' = 94.78801918472° = 94°46'49″ = 1.48773662402 rad
∠ C' = γ' = 94.78801918472° = 94°46'49″ = 1.48773662402 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 = 1 ; ; b = 6 ; ; c = 6 ; ;

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

p = a+b+c = 1+6+6 = 13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13 }{ 2 } = 6.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.5 * (6.5-1)(6.5-6)(6.5-6) } ; ; T = sqrt{ 8.94 } = 2.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.99 }{ 1 } = 5.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.99 }{ 6 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.99 }{ 6 } = 1 ; ;

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{ 1**2-6**2-6**2 }{ 2 * 6 * 6 } ) = 9° 33'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-1**2-6**2 }{ 2 * 1 * 6 } ) = 85° 13'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6**2-1**2-6**2 }{ 2 * 6 * 1 } ) = 85° 13'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.99 }{ 6.5 } = 0.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 9° 33'37" } = 3.01 ; ;




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