2 7 7 triangle

Acute isosceles triangle.

Sides: a = 2   b = 7   c = 7

Area: T = 6.92882032303
Perimeter: p = 16
Semiperimeter: s = 8

Angle ∠ A = α = 16.42664214035° = 16°25'35″ = 0.28766951378 rad
Angle ∠ B = β = 81.78767892983° = 81°47'12″ = 1.42774487579 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 6.92882032303
Height: hb = 1.97994866372
Height: hc = 1.97994866372

Median: ma = 6.92882032303
Median: mb = 3.77549172176
Median: mc = 3.77549172176

Inradius: r = 0.86660254038
Circumradius: R = 3.53662703988

Vertex coordinates: A[7; 0] B[0; 0] C[0.28657142857; 1.97994866372]
Centroid: CG[2.42985714286; 0.66598288791]
Coordinates of the circumscribed circle: U[3.5; 0.50551814855]
Coordinates of the inscribed circle: I[1; 0.86660254038]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.5743578597° = 163°34'25″ = 0.28766951378 rad
∠ B' = β' = 98.21332107017° = 98°12'48″ = 1.42774487579 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 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 = 7 ; ; c = 7 ; ;

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

p = a+b+c = 2+7+7 = 16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16 }{ 2 } = 8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8 * (8-2)(8-7)(8-7) } ; ; T = sqrt{ 48 } = 6.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.93 }{ 2 } = 6.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.93 }{ 7 } = 1.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.93 }{ 7 } = 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**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 16° 25'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-2**2-7**2 }{ 2 * 2 * 7 } ) = 81° 47'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-2**2-7**2 }{ 2 * 7 * 2 } ) = 81° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.93 }{ 8 } = 0.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 16° 25'35" } = 3.54 ; ;




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