18 19 25 triangle

Acute scalene triangle.

Sides: a = 18   b = 19   c = 25

Area: T = 170.3410834799
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 45.82658084437° = 45°49'33″ = 0.87998112397 rad
Angle ∠ B = β = 49.20766050518° = 49°12'24″ = 0.85988172719 rad
Angle ∠ C = γ = 84.96875865045° = 84°58'3″ = 1.4832964142 rad

Height: ha = 18.92767594221
Height: hb = 17.93106141894
Height: hc = 13.62772667839

Median: ma = 20.29877831302
Median: mb = 19.60222957839
Median: mc = 13.6477344064

Inradius: r = 5.49548656387
Circumradius: R = 12.54883710499

Vertex coordinates: A[25; 0] B[0; 0] C[11.76; 13.62772667839]
Centroid: CG[12.25333333333; 4.54224222613]
Coordinates of the circumscribed circle: U[12.5; 1.10107343026]
Coordinates of the inscribed circle: I[12; 5.49548656387]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.1744191556° = 134°10'27″ = 0.87998112397 rad
∠ B' = β' = 130.7933394948° = 130°47'36″ = 0.85988172719 rad
∠ C' = γ' = 95.03224134955° = 95°1'57″ = 1.4832964142 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 = 18 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 18+19+25 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-18)(31-19)(31-25) } ; ; T = sqrt{ 29016 } = 170.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 170.34 }{ 18 } = 18.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 170.34 }{ 19 } = 17.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 170.34 }{ 25 } = 13.63 ; ;

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{ 18**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 45° 49'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 49° 12'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 84° 58'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 170.34 }{ 31 } = 5.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 45° 49'33" } = 12.55 ; ;




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