12 16 18 triangle

Acute scalene triangle.

Sides: a = 12   b = 16   c = 18

Area: T = 94.10110095589
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 40.80444376906° = 40°48'16″ = 0.71221717871 rad
Angle ∠ B = β = 60.61107200521° = 60°36'39″ = 1.05878566269 rad
Angle ∠ C = γ = 78.58548422573° = 78°35'5″ = 1.37215642395 rad

Height: ha = 15.68435015931
Height: hb = 11.76326261949
Height: hc = 10.45656677288

Median: ma = 15.93773774505
Median: mb = 13.03884048104
Median: mc = 10.90987121146

Inradius: r = 4.09113482417
Circumradius: R = 9.18216230671

Vertex coordinates: A[18; 0] B[0; 0] C[5.88988888889; 10.45656677288]
Centroid: CG[7.9632962963; 3.48552225763]
Coordinates of the circumscribed circle: U[9; 1.8177196232]
Coordinates of the inscribed circle: I[7; 4.09113482417]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.1965562309° = 139°11'44″ = 0.71221717871 rad
∠ B' = β' = 119.3899279948° = 119°23'21″ = 1.05878566269 rad
∠ C' = γ' = 101.4155157743° = 101°24'55″ = 1.37215642395 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 = 12 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 12+16+18 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-12)(23-16)(23-18) } ; ; T = sqrt{ 8855 } = 94.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 94.1 }{ 12 } = 15.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 94.1 }{ 16 } = 11.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 94.1 }{ 18 } = 10.46 ; ;

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{ 12**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 40° 48'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 60° 36'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-12**2-16**2 }{ 2 * 16 * 12 } ) = 78° 35'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 94.1 }{ 23 } = 4.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 40° 48'16" } = 9.18 ; ;




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