8 16 18 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 16   c = 18

Area: T = 63.99221870231
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 62.7220387264° = 62°43'13″ = 1.09546772659 rad
Angle ∠ C = γ = 90.89552829866° = 90°53'43″ = 1.58664219626 rad

Height: ha = 15.99880467558
Height: hb = 7.99990233779
Height: hc = 7.11102430026

Median: ma = 16.55329453572
Median: mb = 11.4021754251
Median: mc = 8.88881944173

Inradius: r = 3.04772470011
Circumradius: R = 9.0011098834

Vertex coordinates: A[18; 0] B[0; 0] C[3.66766666667; 7.11102430026]
Centroid: CG[7.22222222222; 2.37700810009]
Coordinates of the circumscribed circle: U[9; -0.14106421693]
Coordinates of the inscribed circle: I[5; 3.04772470011]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 117.2879612736° = 117°16'47″ = 1.09546772659 rad
∠ C' = γ' = 89.10547170134° = 89°6'17″ = 1.58664219626 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 = 8 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 8+16+18 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-8)(21-16)(21-18) } ; ; T = sqrt{ 4095 } = 63.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.99 }{ 8 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.99 }{ 16 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.99 }{ 18 } = 7.11 ; ;

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{ 8**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 26° 23'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 62° 43'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-16**2 }{ 2 * 16 * 8 } ) = 90° 53'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.99 }{ 21 } = 3.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 26° 23'4" } = 9 ; ;




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