2.5 2.5 4.5 triangle

Obtuse isosceles triangle.

Sides: a = 2.5   b = 2.5   c = 4.5

Area: T = 2.45218806557
Perimeter: p = 9.5
Semiperimeter: s = 4.75

Angle ∠ A = α = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ B = β = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ C = γ = 128.3166134474° = 128°18'58″ = 2.243953903 rad

Height: ha = 1.96215045246
Height: hb = 1.96215045246
Height: hc = 1.09897247359

Median: ma = 3.41986985828
Median: mb = 3.41986985828
Median: mc = 1.09897247359

Inradius: r = 0.51661854012
Circumradius: R = 2.86876966734

Vertex coordinates: A[4.5; 0] B[0; 0] C[2.25; 1.09897247359]
Centroid: CG[2.25; 0.36332415786]
Coordinates of the circumscribed circle: U[2.25; -1.77879719375]
Coordinates of the inscribed circle: I[2.25; 0.51661854012]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ B' = β' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ C' = γ' = 51.68438655263° = 51°41'2″ = 2.243953903 rad

Calculate another triangle




How did we calculate this triangle?

a = 2.5 ; ; b = 2.5 ; ; c = 4.5 ; ;

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

p = a+b+c = 2.5+2.5+4.5 = 9.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9.5 }{ 2 } = 4.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.75 * (4.75-2.5)(4.75-2.5)(4.75-4.5) } ; ; T = sqrt{ 6.01 } = 2.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.45 }{ 2.5 } = 1.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.45 }{ 2.5 } = 1.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.45 }{ 4.5 } = 1.09 ; ;

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{ 2.5**2-2.5**2-4.5**2 }{ 2 * 2.5 * 4.5 } ) = 25° 50'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.5**2-2.5**2-4.5**2 }{ 2 * 2.5 * 4.5 } ) = 25° 50'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.5**2-2.5**2-2.5**2 }{ 2 * 2.5 * 2.5 } ) = 128° 18'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.45 }{ 4.75 } = 0.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.5 }{ 2 * sin 25° 50'31" } = 2.87 ; ;

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