240 132 330 triangle

Obtuse scalene triangle.

Sides: a = 240   b = 132   c = 330

Area: T = 13385.87546072
Perimeter: p = 702
Semiperimeter: s = 351

Angle ∠ A = α = 37.92224831781° = 37°55'21″ = 0.6621872192 rad
Angle ∠ B = β = 19.75767220686° = 19°45'24″ = 0.34548198495 rad
Angle ∠ C = γ = 122.3210794753° = 122°19'15″ = 2.13549006121 rad

Height: ha = 111.549895506
Height: hb = 202.8166281928
Height: hc = 81.1276512771

Median: ma = 220.8211194635
Median: mb = 280.8810757618
Median: mc = 101.4254849026

Inradius: r = 38.13663948923
Circumradius: R = 195.2510596371

Vertex coordinates: A[330; 0] B[0; 0] C[225.8732727273; 81.1276512771]
Centroid: CG[185.2910909091; 27.04221709237]
Coordinates of the circumscribed circle: U[165; -104.3932506355]
Coordinates of the inscribed circle: I[219; 38.13663948923]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0787516822° = 142°4'39″ = 0.6621872192 rad
∠ B' = β' = 160.2433277931° = 160°14'36″ = 0.34548198495 rad
∠ C' = γ' = 57.67992052467° = 57°40'45″ = 2.13549006121 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 = 240 ; ; b = 132 ; ; c = 330 ; ;

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

p = a+b+c = 240+132+330 = 702 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 702 }{ 2 } = 351 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 351 * (351-240)(351-132)(351-330) } ; ; T = sqrt{ 179181639 } = 13385.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13385.87 }{ 240 } = 111.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13385.87 }{ 132 } = 202.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13385.87 }{ 330 } = 81.13 ; ;

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{ 132**2+330**2-240**2 }{ 2 * 132 * 330 } ) = 37° 55'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 240**2+330**2-132**2 }{ 2 * 240 * 330 } ) = 19° 45'24" ; ; gamma = 180° - alpha - beta = 180° - 37° 55'21" - 19° 45'24" = 122° 19'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13385.87 }{ 351 } = 38.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 240 }{ 2 * sin 37° 55'21" } = 195.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 132**2+2 * 330**2 - 240**2 } }{ 2 } = 220.821 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 330**2+2 * 240**2 - 132**2 } }{ 2 } = 280.881 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 132**2+2 * 240**2 - 330**2 } }{ 2 } = 101.425 ; ;
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