10 19 19 triangle

Acute isosceles triangle.

Sides: a = 10   b = 19   c = 19

Area: T = 91.65215138991
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 30.51550465809° = 30°30'54″ = 0.53325880342 rad
Angle ∠ B = β = 74.74224767095° = 74°44'33″ = 1.30545023097 rad
Angle ∠ C = γ = 74.74224767095° = 74°44'33″ = 1.30545023097 rad

Height: ha = 18.33303027798
Height: hb = 9.64875277789
Height: hc = 9.64875277789

Median: ma = 18.33303027798
Median: mb = 11.84327192823
Median: mc = 11.84327192823

Inradius: r = 3.81988130791
Circumradius: R = 9.84770822969

Vertex coordinates: A[19; 0] B[0; 0] C[2.63215789474; 9.64875277789]
Centroid: CG[7.21105263158; 3.2165842593]
Coordinates of the circumscribed circle: U[9.5; 2.59113374466]
Coordinates of the inscribed circle: I[5; 3.81988130791]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.4854953419° = 149°29'6″ = 0.53325880342 rad
∠ B' = β' = 105.258752329° = 105°15'27″ = 1.30545023097 rad
∠ C' = γ' = 105.258752329° = 105°15'27″ = 1.30545023097 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 = 10 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 10+19+19 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-10)(24-19)(24-19) } ; ; T = sqrt{ 8400 } = 91.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.65 }{ 10 } = 18.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.65 }{ 19 } = 9.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.65 }{ 19 } = 9.65 ; ;

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{ 10**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 30° 30'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 74° 44'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-19**2 }{ 2 * 19 * 10 } ) = 74° 44'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.65 }{ 24 } = 3.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 30° 30'54" } = 9.85 ; ;




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