5 16 18 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 16   c = 18

Area: T = 38.52883986171
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 15.51990244034° = 15°31'8″ = 0.27108580725 rad
Angle ∠ B = β = 58.89110774895° = 58°53'28″ = 1.02878432022 rad
Angle ∠ C = γ = 105.5989898107° = 105°35'24″ = 1.84328913788 rad

Height: ha = 15.41113594468
Height: hb = 4.81660498271
Height: hc = 4.28109331797

Median: ma = 16.84548805279
Median: mb = 10.51218980208
Median: mc = 7.71436243103

Inradius: r = 1.97658153137
Circumradius: R = 9.34437571485

Vertex coordinates: A[18; 0] B[0; 0] C[2.58333333333; 4.28109331797]
Centroid: CG[6.86111111111; 1.42769777266]
Coordinates of the circumscribed circle: U[9; -2.51111347337]
Coordinates of the inscribed circle: I[3.5; 1.97658153137]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.4810975597° = 164°28'52″ = 0.27108580725 rad
∠ B' = β' = 121.1098922511° = 121°6'32″ = 1.02878432022 rad
∠ C' = γ' = 74.41101018929° = 74°24'36″ = 1.84328913788 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 = 5 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 5+16+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 * (19.5-5)(19.5-16)(19.5-18) } ; ; T = sqrt{ 1484.44 } = 38.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.53 }{ 5 } = 15.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.53 }{ 16 } = 4.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.53 }{ 18 } = 4.28 ; ;

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{ 5**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 15° 31'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-5**2-18**2 }{ 2 * 5 * 18 } ) = 58° 53'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-5**2-16**2 }{ 2 * 16 * 5 } ) = 105° 35'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.53 }{ 19.5 } = 1.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 15° 31'8" } = 9.34 ; ;




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