2.7 3.9 4.3 triangle

Acute scalene triangle.

Sides: a = 2.7   b = 3.9   c = 4.3

Area: T = 5.16986766923
Perimeter: p = 10.9
Semiperimeter: s = 5.45

Angle ∠ A = α = 38.05551291715° = 38°3'18″ = 0.66441873013 rad
Angle ∠ B = β = 62.9211487232° = 62°55'17″ = 1.09881871225 rad
Angle ∠ C = γ = 79.02333835965° = 79°1'24″ = 1.37992182298 rad

Height: ha = 3.82986494017
Height: hb = 2.6510603432
Height: hc = 2.40440356709

Median: ma = 3.87765319552
Median: mb = 3.0154548059
Median: mc = 2.57443931324

Inradius: r = 0.94883810445
Circumradius: R = 2.19900673371

Vertex coordinates: A[4.3; 0] B[0; 0] C[1.22990697674; 2.40440356709]
Centroid: CG[1.84330232558; 0.80113452236]
Coordinates of the circumscribed circle: U[2.15; 0.41770071235]
Coordinates of the inscribed circle: I[1.55; 0.94883810445]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.9454870828° = 141°56'42″ = 0.66441873013 rad
∠ B' = β' = 117.0798512768° = 117°4'43″ = 1.09881871225 rad
∠ C' = γ' = 100.9776616404° = 100°58'36″ = 1.37992182298 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 = 2.7 ; ; b = 3.9 ; ; c = 4.3 ; ;

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

p = a+b+c = 2.7+3.9+4.3 = 10.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.9 }{ 2 } = 5.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.45 * (5.45-2.7)(5.45-3.9)(5.45-4.3) } ; ; T = sqrt{ 26.72 } = 5.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.17 }{ 2.7 } = 3.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.17 }{ 3.9 } = 2.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.17 }{ 4.3 } = 2.4 ; ;

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{ 3.9**2+4.3**2-2.7**2 }{ 2 * 3.9 * 4.3 } ) = 38° 3'18" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.7**2+4.3**2-3.9**2 }{ 2 * 2.7 * 4.3 } ) = 62° 55'17" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 2.7**2+3.9**2-4.3**2 }{ 2 * 2.7 * 3.9 } ) = 79° 1'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.17 }{ 5.45 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.7 }{ 2 * sin 38° 3'18" } = 2.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 4.3**2 - 2.7**2 } }{ 2 } = 3.877 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.3**2+2 * 2.7**2 - 3.9**2 } }{ 2 } = 3.015 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 2.7**2 - 4.3**2 } }{ 2 } = 2.574 ; ;
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