11 16 18 triangle

Acute scalene triangle.

Sides: a = 11   b = 16   c = 18

Area: T = 86.99767671813
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 37.16772854613° = 37°10'2″ = 0.64986915053 rad
Angle ∠ B = β = 61.49325694906° = 61°29'33″ = 1.07332478031 rad
Angle ∠ C = γ = 81.34401450481° = 81°20'25″ = 1.42196533451 rad

Height: ha = 15.8187594033
Height: hb = 10.87545958977
Height: hc = 9.66663074646

Median: ma = 16.11767614613
Median: mb = 12.5989678312
Median: mc = 10.36882206767

Inradius: r = 3.86765229858
Circumradius: R = 9.1043786562

Vertex coordinates: A[18; 0] B[0; 0] C[5.25; 9.66663074646]
Centroid: CG[7.75; 3.22221024882]
Coordinates of the circumscribed circle: U[9; 1.37107405903]
Coordinates of the inscribed circle: I[6.5; 3.86765229858]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.8332714539° = 142°49'58″ = 0.64986915053 rad
∠ B' = β' = 118.5077430509° = 118°30'27″ = 1.07332478031 rad
∠ C' = γ' = 98.66598549519° = 98°39'35″ = 1.42196533451 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 = 16 ; ; c = 18 ; ;

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

p = a+b+c = 11+16+18 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-11)(22.5-16)(22.5-18) } ; ; T = sqrt{ 7568.44 } = 87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87 }{ 11 } = 15.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87 }{ 16 } = 10.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87 }{ 18 } = 9.67 ; ;

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**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 37° 10'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 61° 29'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-16**2 }{ 2 * 16 * 11 } ) = 81° 20'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87 }{ 22.5 } = 3.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 37° 10'2" } = 9.1 ; ;




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