2 8 8 triangle

Acute isosceles triangle.

Sides: a = 2   b = 8   c = 8

Area: T = 7.93772539332
Perimeter: p = 18
Semiperimeter: s = 9

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 82.81992442185° = 82°49'9″ = 1.44554684956 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 7.93772539332
Height: hb = 1.98443134833
Height: hc = 1.98443134833

Median: ma = 7.93772539332
Median: mb = 4.24326406871
Median: mc = 4.24326406871

Inradius: r = 0.88219171037
Circumradius: R = 4.03216210454

Vertex coordinates: A[8; 0] B[0; 0] C[0.25; 1.98443134833]
Centroid: CG[2.75; 0.66114378278]
Coordinates of the circumscribed circle: U[4; 0.50439526307]
Coordinates of the inscribed circle: I[1; 0.88219171037]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 97.18107557815° = 97°10'51″ = 1.44554684956 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 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 = 2 ; ; b = 8 ; ; c = 8 ; ;

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

p = a+b+c = 2+8+8 = 18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18 }{ 2 } = 9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9 * (9-2)(9-8)(9-8) } ; ; T = sqrt{ 63 } = 7.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.94 }{ 2 } = 7.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.94 }{ 8 } = 1.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.94 }{ 8 } = 1.98 ; ;

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{ 2**2-8**2-8**2 }{ 2 * 8 * 8 } ) = 14° 21'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-2**2-8**2 }{ 2 * 2 * 8 } ) = 82° 49'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-2**2-8**2 }{ 2 * 8 * 2 } ) = 82° 49'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.94 }{ 9 } = 0.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 14° 21'41" } = 4.03 ; ;




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