17 19 19 triangle

Acute isosceles triangle.

Sides: a = 17   b = 19   c = 19

Area: T = 144.4377486478
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 53.1549939038° = 53°9' = 0.92876414334 rad
Angle ∠ B = β = 63.4255030481° = 63°25'30″ = 1.10769756101 rad
Angle ∠ C = γ = 63.4255030481° = 63°25'30″ = 1.10769756101 rad

Height: ha = 16.9932645468
Height: hb = 15.2043945945
Height: hc = 15.2043945945

Median: ma = 16.9932645468
Median: mb = 15.3221553446
Median: mc = 15.3221553446

Inradius: r = 5.25222722356
Circumradius: R = 10.62222424484

Vertex coordinates: A[19; 0] B[0; 0] C[7.60552631579; 15.2043945945]
Centroid: CG[8.86884210526; 5.06879819817]
Coordinates of the circumscribed circle: U[9.5; 4.75220558322]
Coordinates of the inscribed circle: I[8.5; 5.25222722356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8550060962° = 126°51' = 0.92876414334 rad
∠ B' = β' = 116.5754969519° = 116°34'30″ = 1.10769756101 rad
∠ C' = γ' = 116.5754969519° = 116°34'30″ = 1.10769756101 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 = 19 ; ; c = 19 ; ;

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

p = a+b+c = 17+19+19 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-17)(27.5-19)(27.5-19) } ; ; T = sqrt{ 20862.19 } = 144.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 144.44 }{ 17 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 144.44 }{ 19 } = 15.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 144.44 }{ 19 } = 15.2 ; ;

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{ 17**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 53° 9' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 63° 25'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-17**2-19**2 }{ 2 * 19 * 17 } ) = 63° 25'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 144.44 }{ 27.5 } = 5.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 53° 9' } = 10.62 ; ;




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