8 11 18 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 11   c = 18

Area: T = 26.99895813232
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 15.82203528829° = 15°49'13″ = 0.27661172466 rad
Angle ∠ B = β = 22.01553695404° = 22°55″ = 0.38442406845 rad
Angle ∠ C = γ = 142.1644277577° = 142°9'51″ = 2.48112347224 rad

Height: ha = 6.74773953308
Height: hb = 4.90771966042
Height: hc = 2.99988423692

Median: ma = 14.37701078632
Median: mb = 12.79664838921
Median: mc = 3.39111649916

Inradius: r = 1.45988962877
Circumradius: R = 14.67223283795

Vertex coordinates: A[18; 0] B[0; 0] C[7.41766666667; 2.99988423692]
Centroid: CG[8.47222222222; 10.9996141231]
Coordinates of the circumscribed circle: U[9; -11.58878047998]
Coordinates of the inscribed circle: I[7.5; 1.45988962877]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.1879647117° = 164°10'47″ = 0.27661172466 rad
∠ B' = β' = 157.985463046° = 157°59'5″ = 0.38442406845 rad
∠ C' = γ' = 37.83657224233° = 37°50'9″ = 2.48112347224 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 = 11 ; ; c = 18 ; ;

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

p = a+b+c = 8+11+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 * (18.5-8)(18.5-11)(18.5-18) } ; ; T = sqrt{ 728.44 } = 26.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.99 }{ 8 } = 6.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.99 }{ 11 } = 4.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.99 }{ 18 } = 3 ; ;

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**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 15° 49'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 22° 55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-11**2 }{ 2 * 11 * 8 } ) = 142° 9'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.99 }{ 18.5 } = 1.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 49'13" } = 14.67 ; ;




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