1.8 2.7 3.6 triangle

Obtuse scalene triangle.

Sides: a = 1.8   b = 2.7   c = 3.6

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

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

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

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

Inradius: r = 0.58109475019
Circumradius: R = 1.85990320062

Vertex coordinates: A[3.6; 0] B[0; 0] C[1.23875; 1.30771318793]
Centroid: CG[1.61325; 0.43657106264]
Coordinates of the circumscribed circle: U[1.8; -0.46547580015]
Coordinates of the inscribed circle: I[1.35; 0.58109475019]

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

Calculate another triangle




How did we calculate this triangle?

a = 1.8 ; ; b = 2.7 ; ; c = 3.6 ; ;

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

p = a+b+c = 1.8+2.7+3.6 = 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 * (4.05-1.8)(4.05-2.7)(4.05-3.6) } ; ; 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 }{ 1.8 } = 2.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.35 }{ 2.7 } = 1.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.35 }{ 3.6 } = 1.31 ; ;

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

6. Inradius

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

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.8 }{ 2 * sin 28° 57'18" } = 1.86 ; ;




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