3 3 5 triangle

Obtuse isosceles triangle.

Sides: a = 3   b = 3   c = 5

Area: T = 4.14657809879
Perimeter: p = 11
Semiperimeter: s = 5.5

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 112.8855380476° = 112°53'7″ = 1.97702215667 rad

Height: ha = 2.7643853992
Height: hb = 2.7643853992
Height: hc = 1.65883123952

Median: ma = 3.84105728739
Median: mb = 3.84105728739
Median: mc = 1.65883123952

Inradius: r = 0.75437783614
Circumradius: R = 2.71436021012

Vertex coordinates: A[5; 0] B[0; 0] C[2.5; 1.65883123952]
Centroid: CG[2.5; 0.55327707984]
Coordinates of the circumscribed circle: U[2.5; -1.0555289706]
Coordinates of the inscribed circle: I[2.5; 0.75437783614]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 67.11546195238° = 67°6'53″ = 1.97702215667 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 = 3 ; ; c = 5 ; ;

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

p = a+b+c = 3+3+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 * (5.5-3)(5.5-3)(5.5-5) } ; ; T = sqrt{ 17.19 } = 4.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.15 }{ 3 } = 2.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.15 }{ 3 } = 2.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.15 }{ 5 } = 1.66 ; ;

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**2-3**2-5**2 }{ 2 * 3 * 5 } ) = 33° 33'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3**2-3**2-5**2 }{ 2 * 3 * 5 } ) = 33° 33'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5**2-3**2-3**2 }{ 2 * 3 * 3 } ) = 112° 53'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.15 }{ 5.5 } = 0.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 33° 33'26" } = 2.71 ; ;




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