3 5 5 triangle

Acute isosceles triangle.

Sides: a = 3   b = 5   c = 5

Area: T = 7.15545440106
Perimeter: p = 13
Semiperimeter: s = 6.5

Angle ∠ A = α = 34.91552062474° = 34°54'55″ = 0.6099385308 rad
Angle ∠ B = β = 72.54223968763° = 72°32'33″ = 1.26661036728 rad
Angle ∠ C = γ = 72.54223968763° = 72°32'33″ = 1.26661036728 rad

Height: ha = 4.77696960071
Height: hb = 2.86218176043
Height: hc = 2.86218176043

Median: ma = 4.77696960071
Median: mb = 3.27987192622
Median: mc = 3.27987192622

Inradius: r = 1.10106990786
Circumradius: R = 2.62107120918

Vertex coordinates: A[5; 0] B[0; 0] C[0.9; 2.86218176043]
Centroid: CG[1.96766666667; 0.95439392014]
Coordinates of the circumscribed circle: U[2.5; 0.78662136275]
Coordinates of the inscribed circle: I[1.5; 1.10106990786]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0854793753° = 145°5'5″ = 0.6099385308 rad
∠ B' = β' = 107.4587603124° = 107°27'27″ = 1.26661036728 rad
∠ C' = γ' = 107.4587603124° = 107°27'27″ = 1.26661036728 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 = 3 ; ; b = 5 ; ; c = 5 ; ;

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

p = a+b+c = 3+5+5 = 13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13 }{ 2 } = 6.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.5 * (6.5-3)(6.5-5)(6.5-5) } ; ; T = sqrt{ 51.19 } = 7.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.15 }{ 3 } = 4.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.15 }{ 5 } = 2.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.15 }{ 5 } = 2.86 ; ;

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{ 3**2-5**2-5**2 }{ 2 * 5 * 5 } ) = 34° 54'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5**2-3**2-5**2 }{ 2 * 3 * 5 } ) = 72° 32'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5**2-3**2-5**2 }{ 2 * 5 * 3 } ) = 72° 32'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.15 }{ 6.5 } = 1.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 34° 54'55" } = 2.62 ; ;




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