4 4 6 triangle

Obtuse isosceles triangle.

Sides: a = 4   b = 4   c = 6

Area: T = 7.93772539332
Perimeter: p = 14
Semiperimeter: s = 7

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 3.96986269666
Height: hb = 3.96986269666
Height: hc = 2.64657513111

Median: ma = 4.69904157598
Median: mb = 4.69904157598
Median: mc = 2.64657513111

Inradius: r = 1.1343893419
Circumradius: R = 3.02437157841

Vertex coordinates: A[6; 0] B[0; 0] C[3; 2.64657513111]
Centroid: CG[3; 0.88219171037]
Coordinates of the circumscribed circle: U[3; -0.3787964473]
Coordinates of the inscribed circle: I[3; 1.1343893419]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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 = 4 ; ; b = 4 ; ; c = 6 ; ;

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

p = a+b+c = 4+4+6 = 14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14 }{ 2 } = 7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7 * (7-4)(7-4)(7-6) } ; ; T = sqrt{ 63 } = 7.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.94 }{ 4 } = 3.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.94 }{ 4 } = 3.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.94 }{ 6 } = 2.65 ; ;

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{ 4**2+6**2-4**2 }{ 2 * 4 * 6 } ) = 41° 24'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+6**2-4**2 }{ 2 * 4 * 6 } ) = 41° 24'35" ; ; gamma = 180° - alpha - beta = 180° - 41° 24'35" - 41° 24'35" = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.94 }{ 7 } = 1.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 41° 24'35" } = 3.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4**2+2 * 6**2 - 4**2 } }{ 2 } = 4.69 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 4**2 - 4**2 } }{ 2 } = 4.69 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4**2+2 * 4**2 - 6**2 } }{ 2 } = 2.646 ; ;
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