26.8 13.6 22.14 triangle

Obtuse scalene triangle.

Sides: a = 26.8   b = 13.6   c = 22.14

Area: T = 150.1665914654
Perimeter: p = 62.54
Semiperimeter: s = 31.27

Angle ∠ A = α = 94.10442034322° = 94°6'15″ = 1.64224281899 rad
Angle ∠ B = β = 30.40884735059° = 30°24'30″ = 0.53107279832 rad
Angle ∠ C = γ = 55.48773230619° = 55°29'14″ = 0.96884364805 rad

Height: ha = 11.20664115414
Height: hb = 22.08332227433
Height: hc = 13.5655123275

Median: ma = 12.5770194907
Median: mb = 23.62113843794
Median: mc = 18.14398759643

Inradius: r = 4.8022235838
Circumradius: R = 13.43444521834

Vertex coordinates: A[22.14; 0] B[0; 0] C[23.11333604336; 13.5655123275]
Centroid: CG[15.08444534779; 4.52217077583]
Coordinates of the circumscribed circle: U[11.07; 7.61218069778]
Coordinates of the inscribed circle: I[17.67; 4.8022235838]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 85.89657965678° = 85°53'45″ = 1.64224281899 rad
∠ B' = β' = 149.5921526494° = 149°35'30″ = 0.53107279832 rad
∠ C' = γ' = 124.5132676938° = 124°30'46″ = 0.96884364805 rad

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How did we calculate this triangle?

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

p = a+b+c = 26.8+13.6+22.14 = 62.54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62.54 }{ 2 } = 31.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.27 * (31.27-26.8)(31.27-13.6)(31.27-22.14) } ; ; T = sqrt{ 22549.8 } = 150.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 150.17 }{ 26.8 } = 11.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 150.17 }{ 13.6 } = 22.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 150.17 }{ 22.14 } = 13.57 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 13.6**2+22.14**2-26.8**2 }{ 2 * 13.6 * 22.14 } ) = 94° 6'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 26.8**2+22.14**2-13.6**2 }{ 2 * 26.8 * 22.14 } ) = 30° 24'30" ; ;
 gamma = 180° - alpha - beta = 180° - 94° 6'15" - 30° 24'30" = 55° 29'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 150.17 }{ 31.27 } = 4.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 26.8 }{ 2 * sin 94° 6'15" } = 13.43 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.6**2+2 * 22.14**2 - 26.8**2 } }{ 2 } = 12.57 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22.14**2+2 * 26.8**2 - 13.6**2 } }{ 2 } = 23.621 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.6**2+2 * 26.8**2 - 22.14**2 } }{ 2 } = 18.14 ; ;
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