2.646 2.449 2.236 triangle

Acute scalene triangle.

Sides: a = 2.6465751   b = 2.449949   c = 2.2366068

Area: T = 2.55495098005
Perimeter: p = 7.3311309
Semiperimeter: s = 3.66656545

Angle ∠ A = α = 68.58332716603° = 68°35' = 1.19770039023 rad
Angle ∠ B = β = 59.53296526719° = 59°31'47″ = 1.03989884417 rad
Angle ∠ C = γ = 51.88770756678° = 51°53'13″ = 0.90656003096 rad

Height: ha = 1.92772484829
Height: hb = 2.08216658165
Height: hc = 2.28803508663

Median: ma = 1.9366491955
Median: mb = 2.12113200872
Median: mc = 2.29112877999

Inradius: r = 0.69655128478
Circumradius: R = 1.42109963723

Vertex coordinates: A[2.2366068; 0] B[0; 0] C[1.34216401457; 2.28803508663]
Centroid: CG[1.19325693819; 0.76601169554]
Coordinates of the circumscribed circle: U[1.1188034; 0.87770579598]
Coordinates of the inscribed circle: I[1.21661645; 0.69655128478]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.417672834° = 111°25' = 1.19770039023 rad
∠ B' = β' = 120.4770347328° = 120°28'13″ = 1.03989884417 rad
∠ C' = γ' = 128.1132924332° = 128°6'47″ = 0.90656003096 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 = 2.65 ; ; b = 2.45 ; ; c = 2.24 ; ;

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

p = a+b+c = 2.65+2.45+2.24 = 7.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.33 }{ 2 } = 3.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.67 * (3.67-2.65)(3.67-2.45)(3.67-2.24) } ; ; T = sqrt{ 6.5 } = 2.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.55 }{ 2.65 } = 1.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.55 }{ 2.45 } = 2.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.55 }{ 2.24 } = 2.28 ; ;

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{ 2.45**2+2.24**2-2.65**2 }{ 2 * 2.45 * 2.24 } ) = 68° 35' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.65**2+2.24**2-2.45**2 }{ 2 * 2.65 * 2.24 } ) = 59° 31'47" ; ; gamma = 180° - alpha - beta = 180° - 68° 35' - 59° 31'47" = 51° 53'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.55 }{ 3.67 } = 0.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.65 }{ 2 * sin 68° 35' } = 1.42 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.45**2+2 * 2.24**2 - 2.65**2 } }{ 2 } = 1.936 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 2.65**2 - 2.45**2 } }{ 2 } = 2.121 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.45**2+2 * 2.65**2 - 2.24**2 } }{ 2 } = 2.291 ; ;
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