19 22 25 triangle

Acute scalene triangle.

Sides: a = 19   b = 22   c = 25

Area: T = 201.6333330578
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ B = β = 58.10111663341° = 58°6'4″ = 1.01440566518 rad
Angle ∠ C = γ = 74.74224767095° = 74°44'33″ = 1.30545023097 rad

Height: ha = 21.22545611135
Height: hb = 18.33303027798
Height: hc = 16.13106664462

Median: ma = 21.54664614264
Median: mb = 19.2877301522
Median: mc = 16.31771688721

Inradius: r = 6.11101009266
Circumradius: R = 12.95766872328

Vertex coordinates: A[25; 0] B[0; 0] C[10.04; 16.13106664462]
Centroid: CG[11.68; 5.37768888154]
Coordinates of the circumscribed circle: U[12.5; 3.41096545349]
Coordinates of the inscribed circle: I[11; 6.11101009266]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ B' = β' = 121.8998833666° = 121°53'56″ = 1.01440566518 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 = 19 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 19+22+25 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-19)(33-22)(33-25) } ; ; T = sqrt{ 40656 } = 201.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 201.63 }{ 19 } = 21.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 201.63 }{ 22 } = 18.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 201.63 }{ 25 } = 16.13 ; ;

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{ 19**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 47° 9'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 58° 6'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-19**2-22**2 }{ 2 * 22 * 19 } ) = 74° 44'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 201.63 }{ 33 } = 6.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 47° 9'23" } = 12.96 ; ;




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