10 18 22 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 18   c = 22

Area: T = 88.74111967465
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 26.6277478393° = 26°37'39″ = 0.46547371695 rad
Angle ∠ B = β = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ C = γ = 99.59440682269° = 99°35'39″ = 1.7388244406 rad

Height: ha = 17.74882393493
Height: hb = 9.86601329718
Height: hc = 8.06773815224

Median: ma = 19.46879223339
Median: mb = 14.52658390463
Median: mc = 9.53993920142

Inradius: r = 3.55496478699
Circumradius: R = 11.15660361624

Vertex coordinates: A[22; 0] B[0; 0] C[5.90990909091; 8.06773815224]
Centroid: CG[9.3033030303; 2.68991271741]
Coordinates of the circumscribed circle: U[11; -1.85993393604]
Coordinates of the inscribed circle: I[7; 3.55496478699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3732521607° = 153°22'21″ = 0.46547371695 rad
∠ B' = β' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ C' = γ' = 80.40659317731° = 80°24'21″ = 1.7388244406 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 = 10 ; ; b = 18 ; ; c = 22 ; ;

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

p = a+b+c = 10+18+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 * (25-10)(25-18)(25-22) } ; ; T = sqrt{ 7875 } = 88.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.74 }{ 10 } = 17.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.74 }{ 18 } = 9.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.74 }{ 22 } = 8.07 ; ;

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{ 10**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 26° 37'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-22**2 }{ 2 * 10 * 22 } ) = 53° 46'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 99° 35'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.74 }{ 25 } = 3.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 26° 37'39" } = 11.16 ; ;




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