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: h_a = 102.2132834865
Height: h_b = 160.0221733273
Height: h_c = 121.2598704716

Median: m_a = 106.2187936338
Median: m_b = 165.7710926281
Median: m_c = 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

Calculate another triangle

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

$a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 122**2+161**2-191**2 }{ 2 * 122 * 161 } ) = 83° 40'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 191**2+161**2-122**2 }{ 2 * 191 * 161 } ) = 39° 24'35" ; ; gamma = 180° - alpha - beta = 180° - 83° 40'50" - 39° 24'35" = 56° 54'35" ; ;$

6. Inradius

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

7. Circumradius

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

8. Calculation of medians

$m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 122**2+2 * 161**2 - 191**2 } }{ 2 } = 106.218 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 161**2+2 * 191**2 - 122**2 } }{ 2 } = 165.771 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 122**2+2 * 191**2 - 161**2 } }{ 2 } = 138.572 ; ;$
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.