1 5 5 triangle

Acute isosceles triangle.

Sides: a = 1   b = 5   c = 5

Area: T = 2.48774685928
Perimeter: p = 11
Semiperimeter: s = 5.5

Angle ∠ A = α = 11.47883409545° = 11°28'42″ = 0.22003348423 rad
Angle ∠ B = β = 84.26108295227° = 84°15'39″ = 1.47106289056 rad
Angle ∠ C = γ = 84.26108295227° = 84°15'39″ = 1.47106289056 rad

Height: ha = 4.97549371855
Height: hb = 0.99549874371
Height: hc = 0.99549874371

Median: ma = 4.97549371855
Median: mb = 2.59880762114
Median: mc = 2.59880762114

Inradius: r = 0.45222670169
Circumradius: R = 2.51325945381

Vertex coordinates: A[5; 0] B[0; 0] C[0.1; 0.99549874371]
Centroid: CG[1.7; 0.3321662479]
Coordinates of the circumscribed circle: U[2.5; 0.25112594538]
Coordinates of the inscribed circle: I[0.5; 0.45222670169]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5221659045° = 168°31'18″ = 0.22003348423 rad
∠ B' = β' = 95.73991704773° = 95°44'21″ = 1.47106289056 rad
∠ C' = γ' = 95.73991704773° = 95°44'21″ = 1.47106289056 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 = 5 ; ; c = 5 ; ;

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

p = a+b+c = 1+5+5 = 11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11 }{ 2 } = 5.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.5 * (5.5-1)(5.5-5)(5.5-5) } ; ; T = sqrt{ 6.19 } = 2.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.49 }{ 1 } = 4.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.49 }{ 5 } = 0.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.49 }{ 5 } = 0.99 ; ;

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**2-5**2-5**2 }{ 2 * 5 * 5 } ) = 11° 28'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5**2-1**2-5**2 }{ 2 * 1 * 5 } ) = 84° 15'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5**2-1**2-5**2 }{ 2 * 5 * 1 } ) = 84° 15'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.49 }{ 5.5 } = 0.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 11° 28'42" } = 2.51 ; ;




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