10 11 18 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 11   c = 18

Area: T = 48.6599768518
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 29.44001972368° = 29°24'1″ = 0.51331302425 rad
Angle ∠ B = β = 32.68334637577° = 32°41' = 0.57704340535 rad
Angle ∠ C = γ = 117.9166339005° = 117°54'59″ = 2.05880283575 rad

Height: ha = 9.72199537036
Height: hb = 8.83663215487
Height: hc = 5.43999742798

Median: ma = 14.05334693226
Median: mb = 13.48114687627
Median: mc = 5.43113902456

Inradius: r = 2.49222958214
Circumradius: R = 10.18552336975

Vertex coordinates: A[18; 0] B[0; 0] C[8.41766666667; 5.43999742798]
Centroid: CG[8.80655555556; 1.87999914266]
Coordinates of the circumscribed circle: U[9; -4.76985412311]
Coordinates of the inscribed circle: I[8.5; 2.49222958214]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6599802763° = 150°35'59″ = 0.51331302425 rad
∠ B' = β' = 147.3176536242° = 147°19' = 0.57704340535 rad
∠ C' = γ' = 62.08436609946° = 62°5'1″ = 2.05880283575 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 = 10 ; ; b = 11 ; ; c = 18 ; ;

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

p = a+b+c = 10+11+18 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-10)(19.5-11)(19.5-18) } ; ; T = sqrt{ 2361.94 } = 48.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.6 }{ 10 } = 9.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.6 }{ 11 } = 8.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.6 }{ 18 } = 5.4 ; ;

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{ 10**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 29° 24'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 32° 41' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-11**2 }{ 2 * 11 * 10 } ) = 117° 54'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.6 }{ 19.5 } = 2.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 29° 24'1" } = 10.19 ; ;




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