2 17 17 triangle

Acute isosceles triangle.

Sides: a = 2   b = 17   c = 17

Area: T = 16.97105627485
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 6.74545733669° = 6°44'40″ = 0.11877150119 rad
Angle ∠ B = β = 86.62877133166° = 86°37'40″ = 1.51219388208 rad
Angle ∠ C = γ = 86.62877133166° = 86°37'40″ = 1.51219388208 rad

Height: ha = 16.97105627485
Height: hb = 1.99765367939
Height: hc = 1.99765367939

Median: ma = 16.97105627485
Median: mb = 8.61768439698
Median: mc = 8.61768439698

Inradius: r = 0.94328090416
Circumradius: R = 8.51547441568

Vertex coordinates: A[17; 0] B[0; 0] C[0.11876470588; 1.99765367939]
Centroid: CG[5.70658823529; 0.66655122646]
Coordinates of the circumscribed circle: U[8.5; 0.50108673033]
Coordinates of the inscribed circle: I[1; 0.94328090416]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.2555426633° = 173°15'20″ = 0.11877150119 rad
∠ B' = β' = 93.37222866834° = 93°22'20″ = 1.51219388208 rad
∠ C' = γ' = 93.37222866834° = 93°22'20″ = 1.51219388208 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 = 2 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 2+17+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-2)(18-17)(18-17) } ; ; T = sqrt{ 288 } = 16.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.97 }{ 2 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.97 }{ 17 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.97 }{ 17 } = 2 ; ;

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{ 2**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 6° 44'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-2**2-17**2 }{ 2 * 2 * 17 } ) = 86° 37'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-2**2-17**2 }{ 2 * 17 * 2 } ) = 86° 37'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.97 }{ 18 } = 0.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 6° 44'40" } = 8.51 ; ;




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