2.94 1.29 2.16 triangle

Obtuse scalene triangle.

Sides: a = 2.94   b = 1.29   c = 2.16

Area: T = 1.26774276762
Perimeter: p = 6.39
Semiperimeter: s = 3.195

Angle ∠ A = α = 114.5332742052° = 114°31'58″ = 1.99989734501 rad
Angle ∠ B = β = 23.52659686628° = 23°31'33″ = 0.41106056129 rad
Angle ∠ C = γ = 41.94112892856° = 41°56'29″ = 0.73220135906 rad

Height: ha = 0.86221956981
Height: hb = 1.96550041491
Height: hc = 1.17435441446

Median: ma = 1.00219730535
Median: mb = 2.49877139548
Median: mc = 1.99768600352

Inradius: r = 0.39766909785
Circumradius: R = 1.61658744506

Vertex coordinates: A[2.16; 0] B[0; 0] C[2.6965625; 1.17435441446]
Centroid: CG[1.61985416667; 0.39111813815]
Coordinates of the circumscribed circle: U[1.08; 1.20219360383]
Coordinates of the inscribed circle: I[1.905; 0.39766909785]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 65.46772579484° = 65°28'2″ = 1.99989734501 rad
∠ B' = β' = 156.4744031337° = 156°28'27″ = 0.41106056129 rad
∠ C' = γ' = 138.0598710714° = 138°3'31″ = 0.73220135906 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 = 2.94 ; ; b = 1.29 ; ; c = 2.16 ; ;

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

p = a+b+c = 2.94+1.29+2.16 = 6.39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.39 }{ 2 } = 3.2 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.2 * (3.2-2.94)(3.2-1.29)(3.2-2.16) } ; ; T = sqrt{ 1.61 } = 1.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.27 }{ 2.94 } = 0.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.27 }{ 1.29 } = 1.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.27 }{ 2.16 } = 1.17 ; ;

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{ 1.29**2+2.16**2-2.94**2 }{ 2 * 1.29 * 2.16 } ) = 114° 31'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.94**2+2.16**2-1.29**2 }{ 2 * 2.94 * 2.16 } ) = 23° 31'33" ; ; gamma = 180° - alpha - beta = 180° - 114° 31'58" - 23° 31'33" = 41° 56'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.27 }{ 3.2 } = 0.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.94 }{ 2 * sin 114° 31'58" } = 1.62 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.29**2+2 * 2.16**2 - 2.94**2 } }{ 2 } = 1.002 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.16**2+2 * 2.94**2 - 1.29**2 } }{ 2 } = 2.498 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.29**2+2 * 2.94**2 - 2.16**2 } }{ 2 } = 1.997 ; ;
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