7 12 18 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 12   c = 18

Area: T = 26.29551991816
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 14.09216737232° = 14°5'30″ = 0.24659461036 rad
Angle ∠ B = β = 24.67695454829° = 24°40'10″ = 0.43105647936 rad
Angle ∠ C = γ = 141.2398780794° = 141°14'20″ = 2.46550817564 rad

Height: ha = 7.51329140519
Height: hb = 4.38325331969
Height: hc = 2.9221688798

Median: ma = 14.89112726118
Median: mb = 12.26878441464
Median: mc = 3.9377003937

Inradius: r = 1.42113621179
Circumradius: R = 14.37552476408

Vertex coordinates: A[18; 0] B[0; 0] C[6.36111111111; 2.9221688798]
Centroid: CG[8.12203703704; 0.9743896266]
Coordinates of the circumscribed circle: U[9; -11.20992704818]
Coordinates of the inscribed circle: I[6.5; 1.42113621179]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.9088326277° = 165°54'30″ = 0.24659461036 rad
∠ B' = β' = 155.3330454517° = 155°19'50″ = 0.43105647936 rad
∠ C' = γ' = 38.76112192061° = 38°45'40″ = 2.46550817564 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 = 7 ; ; b = 12 ; ; c = 18 ; ;

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

p = a+b+c = 7+12+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 * (18.5-7)(18.5-12)(18.5-18) } ; ; T = sqrt{ 691.44 } = 26.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.3 }{ 7 } = 7.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.3 }{ 12 } = 4.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.3 }{ 18 } = 2.92 ; ;

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{ 7**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 14° 5'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-7**2-18**2 }{ 2 * 7 * 18 } ) = 24° 40'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-7**2-12**2 }{ 2 * 12 * 7 } ) = 141° 14'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.3 }{ 18.5 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 5'30" } = 14.38 ; ;




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