9 10 18 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 10   c = 18

Area: T = 27.33301573358
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 17.6788070483° = 17°40'41″ = 0.30985405353 rad
Angle ∠ B = β = 19.71991160383° = 19°43'9″ = 0.34441635005 rad
Angle ∠ C = γ = 142.6032813479° = 142°36'10″ = 2.48988886178 rad

Height: ha = 6.07333682968
Height: hb = 5.46660314672
Height: hc = 3.03766841484

Median: ma = 13.84773824241
Median: mb = 13.32329125945
Median: mc = 3.08222070015

Inradius: r = 1.47773058019
Circumradius: R = 14.81987950411

Vertex coordinates: A[18; 0] B[0; 0] C[8.47222222222; 3.03766841484]
Centroid: CG[8.82440740741; 1.01222280495]
Coordinates of the circumscribed circle: U[9; -11.77327093938]
Coordinates of the inscribed circle: I[8.5; 1.47773058019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.3221929517° = 162°19'19″ = 0.30985405353 rad
∠ B' = β' = 160.2810883962° = 160°16'51″ = 0.34441635005 rad
∠ C' = γ' = 37.39771865213° = 37°23'50″ = 2.48988886178 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 = 10 ; ; c = 18 ; ;

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

p = a+b+c = 9+10+18 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-9)(18.5-10)(18.5-18) } ; ; T = sqrt{ 746.94 } = 27.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.33 }{ 9 } = 6.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.33 }{ 10 } = 5.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.33 }{ 18 } = 3.04 ; ;

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**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 17° 40'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 19° 43'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-10**2 }{ 2 * 10 * 9 } ) = 142° 36'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.33 }{ 18.5 } = 1.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 40'41" } = 14.82 ; ;




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