11 14 18 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 14   c = 18

Area: T = 76.98801110677
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 37.65884620062° = 37°39'30″ = 0.65772641532 rad
Angle ∠ B = β = 51.03992490586° = 51°2'21″ = 0.89108029438 rad
Angle ∠ C = γ = 91.30222889352° = 91°18'8″ = 1.59435255565 rad

Height: ha = 13.99663838305
Height: hb = 10.9977158724
Height: hc = 8.55333456742

Median: ma = 15.15875063912
Median: mb = 13.17219398723
Median: mc = 8.80334084308

Inradius: r = 3.58804702822
Circumradius: R = 9.0022325281

Vertex coordinates: A[18; 0] B[0; 0] C[6.91766666667; 8.55333456742]
Centroid: CG[8.30655555556; 2.85111152247]
Coordinates of the circumscribed circle: U[9; -0.20545983018]
Coordinates of the inscribed circle: I[7.5; 3.58804702822]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.3421537994° = 142°20'30″ = 0.65772641532 rad
∠ B' = β' = 128.9610750941° = 128°57'39″ = 0.89108029438 rad
∠ C' = γ' = 88.69877110648° = 88°41'52″ = 1.59435255565 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 = 18 ; ;

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

p = a+b+c = 11+14+18 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-11)(21.5-14)(21.5-18) } ; ; T = sqrt{ 5925.94 } = 76.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.98 }{ 11 } = 14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.98 }{ 14 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.98 }{ 18 } = 8.55 ; ;

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**2-18**2 }{ 2 * 14 * 18 } ) = 37° 39'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 51° 2'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 91° 18'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.98 }{ 21.5 } = 3.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 37° 39'30" } = 9 ; ;




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