2 17 18 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 17   c = 18

Area: T = 15.13106807514
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 5.67554475446° = 5°40'32″ = 0.09990552462 rad
Angle ∠ B = β = 57.20328317042° = 57°12'10″ = 0.99883777547 rad
Angle ∠ C = γ = 117.1221720751° = 117°7'18″ = 2.04441596527 rad

Height: ha = 15.13106807514
Height: hb = 1.78800800884
Height: hc = 1.68111867502

Median: ma = 17.47985582929
Median: mb = 9.57986220303
Median: mc = 8.09332070281

Inradius: r = 0.81878746352
Circumradius: R = 10.11219045808

Vertex coordinates: A[18; 0] B[0; 0] C[1.08333333333; 1.68111867502]
Centroid: CG[6.36111111111; 0.56603955834]
Coordinates of the circumscribed circle: U[9; -4.6109838853]
Coordinates of the inscribed circle: I[1.5; 0.81878746352]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.3254552455° = 174°19'28″ = 0.09990552462 rad
∠ B' = β' = 122.7977168296° = 122°47'50″ = 0.99883777547 rad
∠ C' = γ' = 62.87882792488° = 62°52'42″ = 2.04441596527 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 = 2 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 2+17+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 * (18.5-2)(18.5-17)(18.5-18) } ; ; T = sqrt{ 228.94 } = 15.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.13 }{ 2 } = 15.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.13 }{ 17 } = 1.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.13 }{ 18 } = 1.68 ; ;

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{ 2**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 5° 40'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-2**2-18**2 }{ 2 * 2 * 18 } ) = 57° 12'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-2**2-17**2 }{ 2 * 17 * 2 } ) = 117° 7'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.13 }{ 18.5 } = 0.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 5° 40'32" } = 10.11 ; ;




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