17 17 20 triangle

Acute isosceles triangle.

Sides: a = 17   b = 17   c = 20

Area: T = 137.4777270849
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 53.96881209275° = 53°58'5″ = 0.94219214013 rad
Angle ∠ B = β = 53.96881209275° = 53°58'5″ = 0.94219214013 rad
Angle ∠ C = γ = 72.06437581449° = 72°3'50″ = 1.2587749851 rad

Height: ha = 16.17437965704
Height: hb = 16.17437965704
Height: hc = 13.74877270849

Median: ma = 16.5
Median: mb = 16.5
Median: mc = 13.74877270849

Inradius: r = 5.09217507722
Circumradius: R = 10.51108283797

Vertex coordinates: A[20; 0] B[0; 0] C[10; 13.74877270849]
Centroid: CG[10; 4.5832575695]
Coordinates of the circumscribed circle: U[10; 3.23768987052]
Coordinates of the inscribed circle: I[10; 5.09217507722]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.0321879072° = 126°1'55″ = 0.94219214013 rad
∠ B' = β' = 126.0321879072° = 126°1'55″ = 0.94219214013 rad
∠ C' = γ' = 107.9366241855° = 107°56'10″ = 1.2587749851 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 = 17 ; ; c = 20 ; ;

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

p = a+b+c = 17+17+20 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-17)(27-17)(27-20) } ; ; T = sqrt{ 18900 } = 137.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.48 }{ 17 } = 16.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.48 }{ 17 } = 16.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.48 }{ 20 } = 13.75 ; ;

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**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 53° 58'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 53° 58'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 72° 3'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.48 }{ 27 } = 5.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 53° 58'5" } = 10.51 ; ;




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