11 14 16 triangle

Acute scalene triangle.

Sides: a = 11   b = 14   c = 16

Area: T = 75.47547474325
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 42.36773658321° = 42°22'3″ = 0.73994500292 rad
Angle ∠ B = β = 59.05656994922° = 59°3'21″ = 1.03107163982 rad
Angle ∠ C = γ = 78.57769346758° = 78°34'37″ = 1.37114262262 rad

Height: ha = 13.72326813514
Height: hb = 10.78221067761
Height: hc = 9.43443434291

Median: ma = 13.99110685796
Median: mb = 11.8111011811
Median: mc = 9.72111110476

Inradius: r = 3.68216949967
Circumradius: R = 8.16216702401

Vertex coordinates: A[16; 0] B[0; 0] C[5.656625; 9.43443434291]
Centroid: CG[7.219875; 3.1454781143]
Coordinates of the circumscribed circle: U[8; 1.61664346904]
Coordinates of the inscribed circle: I[6.5; 3.68216949967]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6332634168° = 137°37'57″ = 0.73994500292 rad
∠ B' = β' = 120.9444300508° = 120°56'39″ = 1.03107163982 rad
∠ C' = γ' = 101.4233065324° = 101°25'23″ = 1.37114262262 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 = 11 ; ; b = 14 ; ; c = 16 ; ;

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

p = a+b+c = 11+14+16 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-11)(20.5-14)(20.5-16) } ; ; T = sqrt{ 5696.44 } = 75.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.47 }{ 11 } = 13.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.47 }{ 14 } = 10.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.47 }{ 16 } = 9.43 ; ;

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**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 42° 22'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-16**2 }{ 2 * 11 * 16 } ) = 59° 3'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 78° 34'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.47 }{ 20.5 } = 3.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 42° 22'3" } = 8.16 ; ;




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