9 16 18 triangle

Acute scalene triangle.

Sides: a = 9   b = 16   c = 18

Area: T = 71.92766119041
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 29.96662882425° = 29°57'59″ = 0.52330103944 rad
Angle ∠ B = β = 62.62108586508° = 62°37'15″ = 1.09329401639 rad
Angle ∠ C = γ = 87.41328531068° = 87°24'46″ = 1.52656420953 rad

Height: ha = 15.98436915342
Height: hb = 8.9910826488
Height: hc = 7.99218457671

Median: ma = 16.42440677057
Median: mb = 11.76986022959
Median: mc = 9.35441434669

Inradius: r = 3.34554238095
Circumradius: R = 9.00991828719

Vertex coordinates: A[18; 0] B[0; 0] C[4.13988888889; 7.99218457671]
Centroid: CG[7.38796296296; 2.6643948589]
Coordinates of the circumscribed circle: U[9; 0.40766645046]
Coordinates of the inscribed circle: I[5.5; 3.34554238095]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0343711758° = 150°2'1″ = 0.52330103944 rad
∠ B' = β' = 117.3799141349° = 117°22'45″ = 1.09329401639 rad
∠ C' = γ' = 92.58771468932° = 92°35'14″ = 1.52656420953 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 = 9 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 9+16+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 * (21.5-9)(21.5-16)(21.5-18) } ; ; T = sqrt{ 5173.44 } = 71.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.93 }{ 9 } = 15.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.93 }{ 16 } = 8.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.93 }{ 18 } = 7.99 ; ;

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{ 9**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 29° 57'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 62° 37'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 87° 24'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.93 }{ 21.5 } = 3.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 29° 57'59" } = 9.01 ; ;




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