11 12 18 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 12   c = 18

Area: T = 64.3310688633
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 36.55993057341° = 36°33'34″ = 0.63880802573 rad
Angle ∠ B = β = 40.5276896475° = 40°31'37″ = 0.70773277791 rad
Angle ∠ C = γ = 102.9143797791° = 102°54'50″ = 1.79661846172 rad

Height: ha = 11.69664888424
Height: hb = 10.72217814388
Height: hc = 7.14878542926

Median: ma = 14.27441024236
Median: mb = 13.65765002837
Median: mc = 7.17663500472

Inradius: r = 3.13880823723
Circumradius: R = 9.23435402064

Vertex coordinates: A[18; 0] B[0; 0] C[8.36111111111; 7.14878542926]
Centroid: CG[8.7877037037; 2.38326180975]
Coordinates of the circumscribed circle: U[9; -2.0643556334]
Coordinates of the inscribed circle: I[8.5; 3.13880823723]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.4410694266° = 143°26'26″ = 0.63880802573 rad
∠ B' = β' = 139.4733103525° = 139°28'23″ = 0.70773277791 rad
∠ C' = γ' = 77.08662022091° = 77°5'10″ = 1.79661846172 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 = 11 ; ; b = 12 ; ; c = 18 ; ;

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

p = a+b+c = 11+12+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-11)(20.5-12)(20.5-18) } ; ; T = sqrt{ 4138.44 } = 64.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.33 }{ 11 } = 11.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.33 }{ 12 } = 10.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.33 }{ 18 } = 7.15 ; ;

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{ 11**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 36° 33'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 40° 31'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-12**2 }{ 2 * 12 * 11 } ) = 102° 54'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.33 }{ 20.5 } = 3.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 36° 33'34" } = 9.23 ; ;




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