12 13 18 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 13   c = 18

Area: T = 77.95215073619
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 41.77884625885° = 41°46'42″ = 0.72991717286 rad
Angle ∠ B = β = 46.20110751782° = 46°12'4″ = 0.80663608798 rad
Angle ∠ C = γ = 92.02204622333° = 92°1'14″ = 1.60660600452 rad

Height: ha = 12.99219178937
Height: hb = 11.99325395941
Height: hc = 8.66112785958

Median: ma = 14.50986181285
Median: mb = 13.84773824241
Median: mc = 8.68990735985

Inradius: r = 3.62656515052
Circumradius: R = 9.00655987852

Vertex coordinates: A[18; 0] B[0; 0] C[8.30655555556; 8.66112785958]
Centroid: CG[8.76985185185; 2.88770928653]
Coordinates of the circumscribed circle: U[9; -0.31875050854]
Coordinates of the inscribed circle: I[8.5; 3.62656515052]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.2221537411° = 138°13'18″ = 0.72991717286 rad
∠ B' = β' = 133.7998924822° = 133°47'56″ = 0.80663608798 rad
∠ C' = γ' = 87.98795377667° = 87°58'46″ = 1.60660600452 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 = 12 ; ; b = 13 ; ; c = 18 ; ;

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

p = a+b+c = 12+13+18 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-12)(21.5-13)(21.5-18) } ; ; T = sqrt{ 6076.44 } = 77.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 77.95 }{ 12 } = 12.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 77.95 }{ 13 } = 11.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 77.95 }{ 18 } = 8.66 ; ;

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{ 12**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 41° 46'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 46° 12'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-12**2-13**2 }{ 2 * 13 * 12 } ) = 92° 1'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 77.95 }{ 21.5 } = 3.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 41° 46'42" } = 9.01 ; ;




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