65 55 113.02 triangle

Obtuse scalene triangle.

Sides: a = 65   b = 55   c = 113.02

Area: T = 1135.045466847
Perimeter: p = 233.02
Semiperimeter: s = 116.51

Angle ∠ A = α = 21.42195907325° = 21°25'11″ = 0.37438423827 rad
Angle ∠ B = β = 187.999653861° = 17°59'59″ = 0.31441532241 rad
Angle ∠ C = γ = 140.5810755407° = 140°34'51″ = 2.45435970468 rad

Height: ha = 34.92444513376
Height: hb = 41.27443515808
Height: hc = 20.0865731171

Median: ma = 82.72224890825
Median: mb = 87.99443759566
Median: mc = 20.77554638937

Inradius: r = 9.74220364644
Circumradius: R = 88.99435240488

Vertex coordinates: A[113.02; 0] B[0; 0] C[61.81987949036; 20.0865731171]
Centroid: CG[58.28795983012; 6.69552437237]
Coordinates of the circumscribed circle: U[56.51; -68.74993070701]
Coordinates of the inscribed circle: I[61.51; 9.74220364644]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.5880409268° = 158°34'49″ = 0.37438423827 rad
∠ B' = β' = 1622.000346139° = 162°1″ = 0.31441532241 rad
∠ C' = γ' = 39.41992445934° = 39°25'9″ = 2.45435970468 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 = 65 ; ; b = 55 ; ; c = 113.02 ; ;

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

p = a+b+c = 65+55+113.02 = 233.02 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 233.02 }{ 2 } = 116.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 116.51 * (116.51-65)(116.51-55)(116.51-113.02) } ; ; T = sqrt{ 1288326.4 } = 1135.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1135.04 }{ 65 } = 34.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1135.04 }{ 55 } = 41.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1135.04 }{ 113.02 } = 20.09 ; ;

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{ 55**2+113.02**2-65**2 }{ 2 * 55 * 113.02 } ) = 21° 25'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 65**2+113.02**2-55**2 }{ 2 * 65 * 113.02 } ) = 17° 59'59" ; ;
 gamma = 180° - alpha - beta = 180° - 21° 25'11" - 17° 59'59" = 140° 34'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1135.04 }{ 116.51 } = 9.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 65 }{ 2 * sin 21° 25'11" } = 88.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 113.02**2 - 65**2 } }{ 2 } = 82.722 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 113.02**2+2 * 65**2 - 55**2 } }{ 2 } = 87.994 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 65**2 - 113.02**2 } }{ 2 } = 20.775 ; ;
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