4 17 18 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 17   c = 18

Area: T = 33.66765635312
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 12.71215526646° = 12°42'42″ = 0.2221858447 rad
Angle ∠ B = β = 69.25876200455° = 69°15'27″ = 1.20987735019 rad
Angle ∠ C = γ = 98.03108272899° = 98°1'51″ = 1.71109607047 rad

Height: ha = 16.83332817656
Height: hb = 3.96107721801
Height: hc = 3.74107292812

Median: ma = 17.39325271309
Median: mb = 9.88768599666
Median: mc = 8.45657672626

Inradius: r = 1.72664904375
Circumradius: R = 9.08991367548

Vertex coordinates: A[18; 0] B[0; 0] C[1.41766666667; 3.74107292812]
Centroid: CG[6.47222222222; 1.24769097604]
Coordinates of the circumscribed circle: U[9; -1.27698058702]
Coordinates of the inscribed circle: I[2.5; 1.72664904375]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.2888447335° = 167°17'18″ = 0.2221858447 rad
∠ B' = β' = 110.7422379954° = 110°44'33″ = 1.20987735019 rad
∠ C' = γ' = 81.96991727101° = 81°58'9″ = 1.71109607047 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 = 4 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 4+17+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 * (19.5-4)(19.5-17)(19.5-18) } ; ; T = sqrt{ 1133.44 } = 33.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.67 }{ 4 } = 16.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.67 }{ 17 } = 3.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.67 }{ 18 } = 3.74 ; ;

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{ 4**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 12° 42'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-4**2-18**2 }{ 2 * 4 * 18 } ) = 69° 15'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-4**2-17**2 }{ 2 * 17 * 4 } ) = 98° 1'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.67 }{ 19.5 } = 1.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 12° 42'42" } = 9.09 ; ;




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