3.53 2.4 5.85 triangle

Obtuse scalene triangle.

Sides: a = 3.53   b = 2.4   c = 5.85

Area: T = 1.39330168125
Perimeter: p = 11.78
Semiperimeter: s = 5.89

Angle ∠ A = α = 11.44554829155° = 11°26'44″ = 0.21997613614 rad
Angle ∠ B = β = 7.75436247459° = 7°45'13″ = 0.13553262808 rad
Angle ∠ C = γ = 160.8010892339° = 160°48'3″ = 2.80765050115 rad

Height: ha = 0.7899244653
Height: hb = 1.16108473438
Height: hc = 0.47662450641

Median: ma = 4.10880439384
Median: mb = 4.68799252131
Median: mc = 0.74548657597

Inradius: r = 0.23765054011
Circumradius: R = 8.8954580373

Vertex coordinates: A[5.85; 0] B[0; 0] C[3.49877264957; 0.47662450641]
Centroid: CG[3.11659088319; 0.15987483547]
Coordinates of the circumscribed circle: U[2.925; -8.43998770831]
Coordinates of the inscribed circle: I[3.49; 0.23765054011]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5554517085° = 168°33'16″ = 0.21997613614 rad
∠ B' = β' = 172.2466375254° = 172°14'47″ = 0.13553262808 rad
∠ C' = γ' = 19.19991076613° = 19°11'57″ = 2.80765050115 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 = 3.53 ; ; b = 2.4 ; ; c = 5.85 ; ;

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

p = a+b+c = 3.53+2.4+5.85 = 11.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.78 }{ 2 } = 5.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.89 * (5.89-3.53)(5.89-2.4)(5.89-5.85) } ; ; T = sqrt{ 1.94 } = 1.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.39 }{ 3.53 } = 0.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.39 }{ 2.4 } = 1.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.39 }{ 5.85 } = 0.48 ; ;

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{ 2.4**2+5.85**2-3.53**2 }{ 2 * 2.4 * 5.85 } ) = 11° 26'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.53**2+5.85**2-2.4**2 }{ 2 * 3.53 * 5.85 } ) = 7° 45'13" ; ;
 gamma = 180° - alpha - beta = 180° - 11° 26'44" - 7° 45'13" = 160° 48'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.39 }{ 5.89 } = 0.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.53 }{ 2 * sin 11° 26'44" } = 8.89 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.4**2+2 * 5.85**2 - 3.53**2 } }{ 2 } = 4.108 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.85**2+2 * 3.53**2 - 2.4**2 } }{ 2 } = 4.68 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.4**2+2 * 3.53**2 - 5.85**2 } }{ 2 } = 0.745 ; ;
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