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: h_a = 10.56875668622
Height: h_b = 5.69902283104
Height: h_c = 4.11096093353

Median: m_a = 15.3055227865
Median: m_b = 12.01104121495
Median: m_c = 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

Calculate another triangle

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

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

6. Inradius

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

7. Circumradius

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

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