5 17 18 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 17   c = 18

Area: T = 42.42664068712
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 16.09989339511° = 16°5'56″ = 0.28109794035 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 93.37222866834° = 93°22'20″ = 1.63296538327 rad

Height: ha = 16.97105627485
Height: hb = 4.99113419848
Height: hc = 4.71440452079

Median: ma = 17.32877234512
Median: mb = 10.11218742081
Median: mc = 8.71877978871

Inradius: r = 2.12113203436
Circumradius: R = 9.01656114601

Vertex coordinates: A[18; 0] B[0; 0] C[1.66766666667; 4.71440452079]
Centroid: CG[6.55655555556; 1.57113484026]
Coordinates of the circumscribed circle: U[9; -0.53303300859]
Coordinates of the inscribed circle: I[3; 2.12113203436]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.9011066049° = 163°54'4″ = 0.28109794035 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 86.62877133166° = 86°37'40″ = 1.63296538327 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 = 17 ; ; c = 18 ; ;

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

p = a+b+c = 5+17+18 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-5)(20-17)(20-18) } ; ; T = sqrt{ 1800 } = 42.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.43 }{ 5 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.43 }{ 17 } = 4.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.43 }{ 18 } = 4.71 ; ;

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**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 16° 5'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-5**2-18**2 }{ 2 * 5 * 18 } ) = 70° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-5**2-17**2 }{ 2 * 17 * 5 } ) = 93° 22'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.43 }{ 20 } = 2.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 16° 5'56" } = 9.02 ; ;




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