16 20 22 triangle

Acute scalene triangle.

Sides: a = 16   b = 20   c = 22

Area: T = 154.1143594468
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 44.46884446032° = 44°28'6″ = 0.77661207716 rad
Angle ∠ B = β = 61.12114535039° = 61°7'17″ = 1.06767706072 rad
Angle ∠ C = γ = 74.41101018929° = 74°24'36″ = 1.29987012748 rad

Height: ha = 19.26441993086
Height: hb = 15.41113594468
Height: hc = 14.01103267699

Median: ma = 19.44222220952
Median: mb = 16.43216767252
Median: mc = 14.38774945699

Inradius: r = 5.31442618782
Circumradius: R = 11.4220147626

Vertex coordinates: A[22; 0] B[0; 0] C[7.72772727273; 14.01103267699]
Centroid: CG[9.90990909091; 4.67701089233]
Coordinates of the circumscribed circle: U[11; 3.06991646745]
Coordinates of the inscribed circle: I[9; 5.31442618782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5321555397° = 135°31'54″ = 0.77661207716 rad
∠ B' = β' = 118.8798546496° = 118°52'43″ = 1.06767706072 rad
∠ C' = γ' = 105.5989898107° = 105°35'24″ = 1.29987012748 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 = 16 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 16+20+22 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-16)(29-20)(29-22) } ; ; T = sqrt{ 23751 } = 154.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 154.11 }{ 16 } = 19.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 154.11 }{ 20 } = 15.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 154.11 }{ 22 } = 14.01 ; ;

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{ 16**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 44° 28'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 61° 7'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 74° 24'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 154.11 }{ 29 } = 5.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 44° 28'6" } = 11.42 ; ;




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