1.6 3.3 2.6 triangle

Obtuse scalene triangle.

Sides: a = 1.6   b = 3.3   c = 2.6

Area: T = 2.04326315747
Perimeter: p = 7.5
Semiperimeter: s = 3.75

Angle ∠ A = α = 28.43334642212° = 28°26' = 0.49662575684 rad
Angle ∠ B = β = 100.8777039604° = 100°52'37″ = 1.76106364808 rad
Angle ∠ C = γ = 50.68994961747° = 50°41'22″ = 0.88546986044 rad

Height: ha = 2.55332894684
Height: hb = 1.23879585301
Height: hc = 1.57112550575

Median: ma = 2.86109439002
Median: mb = 1.39219410907
Median: mc = 2.24438805672

Inradius: r = 0.54547017533
Circumradius: R = 1.68801855227

Vertex coordinates: A[2.6; 0] B[0; 0] C[-0.30219230769; 1.57112550575]
Centroid: CG[0.7666025641; 0.52437516858]
Coordinates of the circumscribed circle: U[1.3; 1.06444357147]
Coordinates of the inscribed circle: I[0.45; 0.54547017533]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.5676535779° = 151°34' = 0.49662575684 rad
∠ B' = β' = 79.12329603959° = 79°7'23″ = 1.76106364808 rad
∠ C' = γ' = 129.3110503825° = 129°18'38″ = 0.88546986044 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 = 1.6 ; ; b = 3.3 ; ; c = 2.6 ; ;

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

p = a+b+c = 1.6+3.3+2.6 = 7.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.5 }{ 2 } = 3.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.75 * (3.75-1.6)(3.75-3.3)(3.75-2.6) } ; ; T = sqrt{ 4.17 } = 2.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.04 }{ 1.6 } = 2.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.04 }{ 3.3 } = 1.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.04 }{ 2.6 } = 1.57 ; ;

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{ 1.6**2-3.3**2-2.6**2 }{ 2 * 3.3 * 2.6 } ) = 28° 26' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.3**2-1.6**2-2.6**2 }{ 2 * 1.6 * 2.6 } ) = 100° 52'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.6**2-1.6**2-3.3**2 }{ 2 * 3.3 * 1.6 } ) = 50° 41'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.04 }{ 3.75 } = 0.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.6 }{ 2 * sin 28° 26' } = 1.68 ; ;




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