240 121 302 triangle

Obtuse scalene triangle.

Sides: a = 240   b = 121   c = 302

Area: T = 13724.27437308
Perimeter: p = 663
Semiperimeter: s = 331.5

Angle ∠ A = α = 48.69901502551° = 48°41'25″ = 0.85498034352 rad
Angle ∠ B = β = 22.25334981628° = 22°15'13″ = 0.3888396813 rad
Angle ∠ C = γ = 109.0566351582° = 109°3'23″ = 1.90333924053 rad

Height: ha = 114.3698947757
Height: hb = 226.8477499682
Height: hc = 90.88992300052

Median: ma = 196.2711495638
Median: mb = 265.9733212937
Median: mc = 115.4110138203

Inradius: r = 41.40105240748
Circumradius: R = 159.7554901644

Vertex coordinates: A[302; 0] B[0; 0] C[222.1244172185; 90.88992300052]
Centroid: CG[174.7088057395; 30.29664100017]
Coordinates of the circumscribed circle: U[151; -52.16596453147]
Coordinates of the inscribed circle: I[210.5; 41.40105240748]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.3109849745° = 131°18'35″ = 0.85498034352 rad
∠ B' = β' = 157.7476501837° = 157°44'47″ = 0.3888396813 rad
∠ C' = γ' = 70.94436484179° = 70°56'37″ = 1.90333924053 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 = 121 ; ; c = 302 ; ;

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

p = a+b+c = 240+121+302 = 663 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 663 }{ 2 } = 331.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 331.5 * (331.5-240)(331.5-121)(331.5-302) } ; ; T = sqrt{ 188355689.44 } = 13724.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13724.27 }{ 240 } = 114.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13724.27 }{ 121 } = 226.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13724.27 }{ 302 } = 90.89 ; ;

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{ 121**2+302**2-240**2 }{ 2 * 121 * 302 } ) = 48° 41'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 240**2+302**2-121**2 }{ 2 * 240 * 302 } ) = 22° 15'13" ; ;
 gamma = 180° - alpha - beta = 180° - 48° 41'25" - 22° 15'13" = 109° 3'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13724.27 }{ 331.5 } = 41.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 240 }{ 2 * sin 48° 41'25" } = 159.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 121**2+2 * 302**2 - 240**2 } }{ 2 } = 196.271 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 302**2+2 * 240**2 - 121**2 } }{ 2 } = 265.973 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 121**2+2 * 240**2 - 302**2 } }{ 2 } = 115.41 ; ;
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