3.6 2.7 1.8 triangle

Obtuse scalene triangle.

Sides: a = 3.6   b = 2.7   c = 1.8

Area: T = 2.35328373828
Perimeter: p = 8.1
Semiperimeter: s = 4.05

Angle ∠ A = α = 104.4787512186° = 104°28'39″ = 1.82334765819 rad
Angle ∠ B = β = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ C = γ = 28.95550243719° = 28°57'18″ = 0.50553605103 rad

Height: ha = 1.30771318793
Height: hb = 1.74328425058
Height: hc = 2.61442637587

Median: ma = 1.42330249471
Median: mb = 2.50554939633
Median: mc = 3.05220484924

Inradius: r = 0.58109475019
Circumradius: R = 1.85990320062

Vertex coordinates: A[1.8; 0] B[0; 0] C[2.475; 2.61442637587]
Centroid: CG[1.425; 0.87114212529]
Coordinates of the circumscribed circle: U[0.9; 1.62766530054]
Coordinates of the inscribed circle: I[1.35; 0.58109475019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 75.52224878141° = 75°31'21″ = 1.82334765819 rad
∠ B' = β' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ C' = γ' = 151.0454975628° = 151°2'42″ = 0.50553605103 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 = 3.6 ; ; b = 2.7 ; ; c = 1.8 ; ;

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

p = a+b+c = 3.6+2.7+1.8 = 8.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.1 }{ 2 } = 4.05 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.05 * (4.05-3.6)(4.05-2.7)(4.05-1.8) } ; ; T = sqrt{ 5.54 } = 2.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.35 }{ 3.6 } = 1.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.35 }{ 2.7 } = 1.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.35 }{ 1.8 } = 2.61 ; ;

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{ 2.7**2+1.8**2-3.6**2 }{ 2 * 2.7 * 1.8 } ) = 104° 28'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.6**2+1.8**2-2.7**2 }{ 2 * 3.6 * 1.8 } ) = 46° 34'3" ; ; gamma = 180° - alpha - beta = 180° - 104° 28'39" - 46° 34'3" = 28° 57'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.35 }{ 4.05 } = 0.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.6 }{ 2 * sin 104° 28'39" } = 1.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.7**2+2 * 1.8**2 - 3.6**2 } }{ 2 } = 1.423 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.8**2+2 * 3.6**2 - 2.7**2 } }{ 2 } = 2.505 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.7**2+2 * 3.6**2 - 1.8**2 } }{ 2 } = 3.052 ; ;
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