7 13 18 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 13   c = 18

Area: T = 36.98664840178
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 18.42986696038° = 18°25'43″ = 0.32216409613 rad
Angle ∠ B = β = 35.95105676196° = 35°57'2″ = 0.62774557729 rad
Angle ∠ C = γ = 125.6210762777° = 125°37'15″ = 2.19224959193 rad

Height: ha = 10.56875668622
Height: hb = 5.69902283104
Height: hc = 4.11096093353

Median: ma = 15.3055227865
Median: mb = 12.01104121495
Median: mc = 5.29215026221

Inradius: r = 1.94766570536
Circumradius: R = 11.07216119922

Vertex coordinates: A[18; 0] B[0; 0] C[5.66766666667; 4.11096093353]
Centroid: CG[7.88988888889; 1.37698697784]
Coordinates of the circumscribed circle: U[9; -6.44883014899]
Coordinates of the inscribed circle: I[6; 1.94766570536]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5711330396° = 161°34'17″ = 0.32216409613 rad
∠ B' = β' = 144.049943238° = 144°2'58″ = 0.62774557729 rad
∠ C' = γ' = 54.37992372234° = 54°22'45″ = 2.19224959193 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 = 13 ; ; c = 18 ; ;

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

p = a+b+c = 7+13+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-7)(19-13)(19-18) } ; ; T = sqrt{ 1368 } = 36.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.99 }{ 7 } = 10.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.99 }{ 13 } = 5.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.99 }{ 18 } = 4.11 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 13**2+18**2-7**2 }{ 2 * 13 * 18 } ) = 18° 25'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+18**2-13**2 }{ 2 * 7 * 18 } ) = 35° 57'2" ; ; gamma = 180° - alpha - beta = 180° - 18° 25'43" - 35° 57'2" = 125° 37'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.99 }{ 19 } = 1.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 18° 25'43" } = 11.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 18**2 - 7**2 } }{ 2 } = 15.305 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 7**2 - 13**2 } }{ 2 } = 12.01 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 7**2 - 18**2 } }{ 2 } = 5.292 ; ;
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