17 20 22 triangle

Acute scalene triangle.

Sides: a = 17   b = 20   c = 22

Area: T = 162.0910831018
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 47.45875423466° = 47°27'27″ = 0.82882903689 rad
Angle ∠ B = β = 60.08884091405° = 60°5'18″ = 1.04987405818 rad
Angle ∠ C = γ = 72.45440485129° = 72°27'15″ = 1.26545617029 rad

Height: ha = 19.07695095315
Height: hb = 16.20990831018
Height: hc = 14.73655300925

Median: ma = 19.2298884523
Median: mb = 16.92663108798
Median: mc = 14.95499163877

Inradius: r = 5.49546044413
Circumradius: R = 11.53767413953

Vertex coordinates: A[22; 0] B[0; 0] C[8.47772727273; 14.73655300925]
Centroid: CG[10.15990909091; 4.91218433642]
Coordinates of the circumscribed circle: U[11; 3.47879882148]
Coordinates of the inscribed circle: I[9.5; 5.49546044413]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.5422457653° = 132°32'33″ = 0.82882903689 rad
∠ B' = β' = 119.9121590859° = 119°54'42″ = 1.04987405818 rad
∠ C' = γ' = 107.5465951487° = 107°32'45″ = 1.26545617029 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 = 17 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 17+20+22 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-17)(29.5-20)(29.5-22) } ; ; T = sqrt{ 26273.44 } = 162.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 162.09 }{ 17 } = 19.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 162.09 }{ 20 } = 16.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 162.09 }{ 22 } = 14.74 ; ;

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{ 17**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 47° 27'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 60° 5'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 72° 27'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 162.09 }{ 29.5 } = 5.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 47° 27'27" } = 11.54 ; ;




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