6 16 18 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 16   c = 18

Area: T = 47.32986382648
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 99.59440682269° = 99°35'39″ = 1.7388244406 rad

Height: ha = 15.77662127549
Height: hb = 5.91660797831
Height: hc = 5.2598737585

Median: ma = 16.76330546142
Median: mb = 10.77703296143
Median: mc = 8.06222577483

Inradius: r = 2.36664319132
Circumradius: R = 9.12876659511

Vertex coordinates: A[18; 0] B[0; 0] C[2.88988888889; 5.2598737585]
Centroid: CG[6.9632962963; 1.75329125283]
Coordinates of the circumscribed circle: U[9; -1.52112776585]
Coordinates of the inscribed circle: I[4; 2.36664319132]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 80.40659317731° = 80°24'21″ = 1.7388244406 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 = 6 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 6+16+18 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-6)(20-16)(20-18) } ; ; T = sqrt{ 2240 } = 47.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.33 }{ 6 } = 15.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.33 }{ 16 } = 5.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.33 }{ 18 } = 5.26 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 16**2+18**2-6**2 }{ 2 * 16 * 18 } ) = 19° 11'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+18**2-16**2 }{ 2 * 6 * 18 } ) = 61° 13'4" ; ; gamma = 180° - alpha - beta = 180° - 19° 11'17" - 61° 13'4" = 99° 35'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.33 }{ 20 } = 2.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 19° 11'17" } = 9.13 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 18**2 - 6**2 } }{ 2 } = 16.763 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 6**2 - 16**2 } }{ 2 } = 10.77 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 6**2 - 18**2 } }{ 2 } = 8.062 ; ;
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