17 17 19 triangle

Acute isosceles triangle.

Sides: a = 17   b = 17   c = 19

Area: T = 133.9329785709
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 56.02655240497° = 56°1'32″ = 0.97878298598 rad
Angle ∠ B = β = 56.02655240497° = 56°1'32″ = 0.97878298598 rad
Angle ∠ C = γ = 67.94989519006° = 67°56'56″ = 1.18659329339 rad

Height: ha = 15.75664453775
Height: hb = 15.75664453775
Height: hc = 14.09878721799

Median: ma = 15.89881130956
Median: mb = 15.89881130956
Median: mc = 14.09878721799

Inradius: r = 5.05439541777
Circumradius: R = 10.25497737358

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 14.09878721799]
Centroid: CG[9.5; 4.69992907266]
Coordinates of the circumscribed circle: U[9.5; 3.84880984441]
Coordinates of the inscribed circle: I[9.5; 5.05439541777]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.974447595° = 123°58'28″ = 0.97878298598 rad
∠ B' = β' = 123.974447595° = 123°58'28″ = 0.97878298598 rad
∠ C' = γ' = 112.0511048099° = 112°3'4″ = 1.18659329339 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 = 19 ; ;

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

p = a+b+c = 17+17+19 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-17)(26.5-17)(26.5-19) } ; ; T = sqrt{ 17937.19 } = 133.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.93 }{ 17 } = 15.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.93 }{ 17 } = 15.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.93 }{ 19 } = 14.1 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 17**2+19**2-17**2 }{ 2 * 17 * 19 } ) = 56° 1'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+19**2-17**2 }{ 2 * 17 * 19 } ) = 56° 1'32" ; ; gamma = 180° - alpha - beta = 180° - 56° 1'32" - 56° 1'32" = 67° 56'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.93 }{ 26.5 } = 5.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 56° 1'32" } = 10.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 19**2 - 17**2 } }{ 2 } = 15.898 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 17**2 - 17**2 } }{ 2 } = 15.898 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 17**2 - 19**2 } }{ 2 } = 14.098 ; ;
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