1 17 17 triangle

Acute isosceles triangle.

Sides: a = 1   b = 17   c = 17

Area: T = 8.4966322734
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 3.37108260805° = 3°22'15″ = 0.05988320136 rad
Angle ∠ B = β = 88.31545869598° = 88°18'53″ = 1.541138032 rad
Angle ∠ C = γ = 88.31545869598° = 88°18'53″ = 1.541138032 rad

Height: ha = 16.9932645468
Height: hb = 10.9995673805
Height: hc = 10.9995673805

Median: ma = 16.9932645468
Median: mb = 8.52993610546
Median: mc = 8.52993610546

Inradius: r = 0.48655041562
Circumradius: R = 8.50436788576

Vertex coordinates: A[17; 0] B[0; 0] C[0.02994117647; 10.9995673805]
Centroid: CG[5.67664705882; 0.33331891268]
Coordinates of the circumscribed circle: U[8.5; 0.25501082017]
Coordinates of the inscribed circle: I[0.5; 0.48655041562]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.629917392° = 176°37'45″ = 0.05988320136 rad
∠ B' = β' = 91.68554130402° = 91°41'7″ = 1.541138032 rad
∠ C' = γ' = 91.68554130402° = 91°41'7″ = 1.541138032 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 = 1 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 1+17+17 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-1)(17.5-17)(17.5-17) } ; ; T = sqrt{ 72.19 } = 8.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.5 }{ 1 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.5 }{ 17 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.5 }{ 17 } = 1 ; ;

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{ 1**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 3° 22'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-1**2-17**2 }{ 2 * 1 * 17 } ) = 88° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-1**2-17**2 }{ 2 * 17 * 1 } ) = 88° 18'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.5 }{ 17.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 3° 22'15" } = 8.5 ; ;




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