17 27 27 triangle

Acute isosceles triangle.

Sides: a = 17   b = 27   c = 27

Area: T = 217.8310639489
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 36.69992693976° = 36°41'57″ = 0.64105230841 rad
Angle ∠ B = β = 71.65503653012° = 71°39'1″ = 1.25105347848 rad
Angle ∠ C = γ = 71.65503653012° = 71°39'1″ = 1.25105347848 rad

Height: ha = 25.62771340575
Height: hb = 16.13656029251
Height: hc = 16.13656029251

Median: ma = 25.62771340575
Median: mb = 18.07662274825
Median: mc = 18.07662274825

Inradius: r = 6.13660743518
Circumradius: R = 14.22332057312

Vertex coordinates: A[27; 0] B[0; 0] C[5.35218518519; 16.13656029251]
Centroid: CG[10.78439506173; 5.37985343084]
Coordinates of the circumscribed circle: U[13.5; 4.47876758783]
Coordinates of the inscribed circle: I[8.5; 6.13660743518]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.3010730602° = 143°18'3″ = 0.64105230841 rad
∠ B' = β' = 108.3549634699° = 108°20'59″ = 1.25105347848 rad
∠ C' = γ' = 108.3549634699° = 108°20'59″ = 1.25105347848 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 = 17 ; ; b = 27 ; ; c = 27 ; ;

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

p = a+b+c = 17+27+27 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-17)(35.5-27)(35.5-27) } ; ; T = sqrt{ 47450.19 } = 217.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 217.83 }{ 17 } = 25.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 217.83 }{ 27 } = 16.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 217.83 }{ 27 } = 16.14 ; ;

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{ 17**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 36° 41'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 71° 39'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-17**2-27**2 }{ 2 * 27 * 17 } ) = 71° 39'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 217.83 }{ 35.5 } = 6.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 36° 41'57" } = 14.22 ; ;




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