4 19 22 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 19   c = 22

Area: T = 26.99895813232
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 7.42197114187° = 7°25'11″ = 0.12994983938 rad
Angle ∠ B = β = 37.83657224233° = 37°50'9″ = 0.66603579312 rad
Angle ∠ C = γ = 134.7454566158° = 134°44'40″ = 2.35217363286 rad

Height: ha = 13.49547906616
Height: hb = 2.84110085603
Height: hc = 2.45435983021

Median: ma = 20.45772725455
Median: mb = 12.63992246598
Median: mc = 8.21658383626

Inradius: r = 1.21995369477
Circumradius: R = 15.4877457734

Vertex coordinates: A[22; 0] B[0; 0] C[3.15990909091; 2.45435983021]
Centroid: CG[8.38663636364; 0.81878661007]
Coordinates of the circumscribed circle: U[11; -10.90223551154]
Coordinates of the inscribed circle: I[3.5; 1.21995369477]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.5880288581° = 172°34'49″ = 0.12994983938 rad
∠ B' = β' = 142.1644277577° = 142°9'51″ = 0.66603579312 rad
∠ C' = γ' = 45.2555433842° = 45°15'20″ = 2.35217363286 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 = 4 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 4+19+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-4)(22.5-19)(22.5-22) } ; ; T = sqrt{ 728.44 } = 26.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.99 }{ 4 } = 13.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.99 }{ 19 } = 2.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.99 }{ 22 } = 2.45 ; ;

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{ 4**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 7° 25'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-4**2-22**2 }{ 2 * 4 * 22 } ) = 37° 50'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-4**2-19**2 }{ 2 * 19 * 4 } ) = 134° 44'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.99 }{ 22.5 } = 1.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 25'11" } = 15.49 ; ;




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