19 22 29 triangle

Acute scalene triangle.

Sides: a = 19   b = 22   c = 29

Area: T = 208.9987607642
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 40.93221558081° = 40°55'56″ = 0.71444008888 rad
Angle ∠ B = β = 49.34219877236° = 49°20'31″ = 0.86111801453 rad
Angle ∠ C = γ = 89.72658564683° = 89°43'33″ = 1.56660116195 rad

Height: ha = 221.9997481728
Height: hb = 198.9997825129
Height: hc = 14.41436281132

Median: ma = 23.92217474278
Median: mb = 21.90989023002
Median: mc = 14.56988022843

Inradius: r = 5.97113602183
Circumradius: R = 14.55001659789

Vertex coordinates: A[29; 0] B[0; 0] C[12.37993103448; 14.41436281132]
Centroid: CG[13.79331034483; 4.80545427044]
Coordinates of the circumscribed circle: U[14.5; 0.06993787846]
Coordinates of the inscribed circle: I[13; 5.97113602183]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0687844192° = 139°4'4″ = 0.71444008888 rad
∠ B' = β' = 130.6588012276° = 130°39'29″ = 0.86111801453 rad
∠ C' = γ' = 90.27441435317° = 90°16'27″ = 1.56660116195 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 = 29 ; ;

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

p = a+b+c = 19+22+29 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-19)(35-22)(35-29) } ; ; T = sqrt{ 43680 } = 209 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 209 }{ 19 } = 22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 209 }{ 22 } = 19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 209 }{ 29 } = 14.41 ; ;

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**2-29**2 }{ 2 * 22 * 29 } ) = 40° 55'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 49° 20'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-22**2 }{ 2 * 22 * 19 } ) = 89° 43'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 209 }{ 35 } = 5.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 40° 55'56" } = 14.5 ; ;




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