11.4 13.7 12.2 triangle

Acute scalene triangle.

Sides: a = 11.4   b = 13.7   c = 12.2

Area: T = 65.70438590476
Perimeter: p = 37.3
Semiperimeter: s = 18.65

Angle ∠ A = α = 51.83330483861° = 51°49'59″ = 0.90546573557 rad
Angle ∠ B = β = 70.8880147404° = 70°52'49″ = 1.23770919465 rad
Angle ∠ C = γ = 57.28768042099° = 57°17'12″ = 10.9998433514 rad

Height: ha = 11.52769928154
Height: hb = 9.59218042405
Height: hc = 10.7711124434

Median: ma = 11.6522253001
Median: mb = 9.61765222404
Median: mc = 11.02879191147

Inradius: r = 3.52329951232
Circumradius: R = 7.25499394542

Vertex coordinates: A[12.2; 0] B[0; 0] C[3.73440163934; 10.7711124434]
Centroid: CG[5.31113387978; 3.59903748113]
Coordinates of the circumscribed circle: U[6.1; 3.9188114609]
Coordinates of the inscribed circle: I[4.95; 3.52329951232]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.1676951614° = 128°10'1″ = 0.90546573557 rad
∠ B' = β' = 109.1219852596° = 109°7'11″ = 1.23770919465 rad
∠ C' = γ' = 122.713319579° = 122°42'48″ = 10.9998433514 rad

Calculate another triangle




How did we calculate this triangle?

a = 11.4 ; ; b = 13.7 ; ; c = 12.2 ; ;

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

p = a+b+c = 11.4+13.7+12.2 = 37.3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37.3 }{ 2 } = 18.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.65 * (18.65-11.4)(18.65-13.7)(18.65-12.2) } ; ; T = sqrt{ 4317 } = 65.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.7 }{ 11.4 } = 11.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.7 }{ 13.7 } = 9.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.7 }{ 12.2 } = 10.77 ; ;

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{ 11.4**2-13.7**2-12.2**2 }{ 2 * 13.7 * 12.2 } ) = 51° 49'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.7**2-11.4**2-12.2**2 }{ 2 * 11.4 * 12.2 } ) = 70° 52'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.2**2-11.4**2-13.7**2 }{ 2 * 13.7 * 11.4 } ) = 57° 17'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.7 }{ 18.65 } = 3.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.4 }{ 2 * sin 51° 49'59" } = 7.25 ; ;




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