8 20 22 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 20   c = 22

Area: T = 79.84435971134
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 21.28799664684° = 21°16'48″ = 0.37114054796 rad
Angle ∠ B = β = 65.13767118331° = 65°8'12″ = 1.13768500854 rad
Angle ∠ C = γ = 93.58333216985° = 93°35' = 1.63333370886 rad

Height: ha = 19.96108992783
Height: hb = 7.98443597113
Height: hc = 7.25985088285

Median: ma = 20.64397674406
Median: mb = 13.19109059583
Median: mc = 10.53656537529

Inradius: r = 3.19437438845
Circumradius: R = 11.02215475231

Vertex coordinates: A[22; 0] B[0; 0] C[3.36436363636; 7.25985088285]
Centroid: CG[8.45545454545; 2.42195029428]
Coordinates of the circumscribed circle: U[11; -0.68988467202]
Coordinates of the inscribed circle: I[5; 3.19437438845]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.7220033532° = 158°43'12″ = 0.37114054796 rad
∠ B' = β' = 114.8633288167° = 114°51'48″ = 1.13768500854 rad
∠ C' = γ' = 86.41766783015° = 86°25' = 1.63333370886 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 = 8 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 8+20+22 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-8)(25-20)(25-22) } ; ; T = sqrt{ 6375 } = 79.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.84 }{ 8 } = 19.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.84 }{ 20 } = 7.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.84 }{ 22 } = 7.26 ; ;

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{ 8**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 21° 16'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-8**2-22**2 }{ 2 * 8 * 22 } ) = 65° 8'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-8**2-20**2 }{ 2 * 20 * 8 } ) = 93° 35' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.84 }{ 25 } = 3.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 21° 16'48" } = 11.02 ; ;




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