3 19 19 triangle

Acute isosceles triangle.

Sides: a = 3   b = 19   c = 19

Area: T = 28.41110453873
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 9.05661260276° = 9°3'22″ = 0.15880592167 rad
Angle ∠ B = β = 85.47219369862° = 85°28'19″ = 1.49217667185 rad
Angle ∠ C = γ = 85.47219369862° = 85°28'19″ = 1.49217667185 rad

Height: ha = 18.94106969249
Height: hb = 2.99106363566
Height: hc = 2.99106363566

Median: ma = 18.94106969249
Median: mb = 9.7343961167
Median: mc = 9.7343961167

Inradius: r = 1.3865904653
Circumradius: R = 9.53297443761

Vertex coordinates: A[19; 0] B[0; 0] C[0.23768421053; 2.99106363566]
Centroid: CG[6.41222807018; 0.99768787855]
Coordinates of the circumscribed circle: U[9.5; 0.75223482402]
Coordinates of the inscribed circle: I[1.5; 1.3865904653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.9443873972° = 170°56'38″ = 0.15880592167 rad
∠ B' = β' = 94.52880630138° = 94°31'41″ = 1.49217667185 rad
∠ C' = γ' = 94.52880630138° = 94°31'41″ = 1.49217667185 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 = 3 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 3+19+19 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-3)(20.5-19)(20.5-19) } ; ; T = sqrt{ 807.19 } = 28.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.41 }{ 3 } = 18.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.41 }{ 19 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.41 }{ 19 } = 2.99 ; ;

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{ 3**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 9° 3'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-3**2-19**2 }{ 2 * 3 * 19 } ) = 85° 28'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-3**2-19**2 }{ 2 * 19 * 3 } ) = 85° 28'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.41 }{ 20.5 } = 1.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 9° 3'22" } = 9.53 ; ;




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