2 4 4 triangle

Acute isosceles triangle.

Sides: a = 2   b = 4   c = 4

Area: T = 3.87329833462
Perimeter: p = 10
Semiperimeter: s = 5

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 3.87329833462
Height: hb = 1.93664916731
Height: hc = 1.93664916731

Median: ma = 3.87329833462
Median: mb = 2.44994897428
Median: mc = 2.44994897428

Inradius: r = 0.77545966692
Circumradius: R = 2.0665591118

Vertex coordinates: A[4; 0] B[0; 0] C[0.5; 1.93664916731]
Centroid: CG[1.5; 0.64554972244]
Coordinates of the circumscribed circle: U[2; 0.51663977795]
Coordinates of the inscribed circle: I[1; 0.77545966692]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 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 = 4 ; ; c = 4 ; ;

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

p = a+b+c = 2+4+4 = 10 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10 }{ 2 } = 5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5 * (5-2)(5-4)(5-4) } ; ; T = sqrt{ 15 } = 3.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.87 }{ 2 } = 3.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.87 }{ 4 } = 1.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.87 }{ 4 } = 1.94 ; ;

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**2-4**2-4**2 }{ 2 * 4 * 4 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-2**2-4**2 }{ 2 * 2 * 4 } ) = 75° 31'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4**2-2**2-4**2 }{ 2 * 4 * 2 } ) = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.87 }{ 5 } = 0.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 28° 57'18" } = 2.07 ; ;




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