191 122 161 triangle

Acute scalene triangle.

Sides: a = 191   b = 122   c = 161

Area: T = 9761.326572963
Perimeter: p = 474
Semiperimeter: s = 237

Angle ∠ A = α = 83.68106343729° = 83°40'50″ = 1.461050259 rad
Angle ∠ B = β = 39.41097743666° = 39°24'35″ = 0.68878303202 rad
Angle ∠ C = γ = 56.91095912606° = 56°54'35″ = 0.99332597435 rad

Height: ha = 102.2132834865
Height: hb = 160.0221733273
Height: hc = 121.2598704716

Median: ma = 106.2187936338
Median: mb = 165.7710926281
Median: mc = 138.5722183356

Inradius: r = 41.18770283951
Circumradius: R = 96.08438236504

Vertex coordinates: A[161; 0] B[0; 0] C[147.5711428571; 121.2598704716]
Centroid: CG[102.8577142857; 40.42195682386]
Coordinates of the circumscribed circle: U[80.5; 52.45880896266]
Coordinates of the inscribed circle: I[115; 41.18770283951]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 96.31993656271° = 96°19'10″ = 1.461050259 rad
∠ B' = β' = 140.5990225633° = 140°35'25″ = 0.68878303202 rad
∠ C' = γ' = 123.0990408739° = 123°5'25″ = 0.99332597435 rad

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How did we calculate this triangle?

a = 191 ; ; b = 122 ; ; c = 161 ; ;

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

p = a+b+c = 191+122+161 = 474 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 474 }{ 2 } = 237 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 237 * (237-191)(237-122)(237-161) } ; ; T = sqrt{ 95283480 } = 9761.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9761.33 }{ 191 } = 102.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9761.33 }{ 122 } = 160.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9761.33 }{ 161 } = 121.26 ; ;

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{ 191**2-122**2-161**2 }{ 2 * 122 * 161 } ) = 83° 40'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 122**2-191**2-161**2 }{ 2 * 191 * 161 } ) = 39° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 161**2-191**2-122**2 }{ 2 * 122 * 191 } ) = 56° 54'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9761.33 }{ 237 } = 41.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 191 }{ 2 * sin 83° 40'50" } = 96.08 ; ;




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