10 13 18 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 13   c = 18

Area: T = 63.52990287979
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 32.88769467704° = 32°53'13″ = 0.57439855021 rad
Angle ∠ B = β = 44.90105279607° = 44°54'2″ = 0.78436620488 rad
Angle ∠ C = γ = 102.2132525269° = 102°12'45″ = 1.78439451027 rad

Height: ha = 12.70658057596
Height: hb = 9.77436967381
Height: hc = 7.05987809775

Median: ma = 14.88328760661
Median: mb = 13.02988142208
Median: mc = 7.31443694192

Inradius: r = 3.09989770145
Circumradius: R = 9.20883888432

Vertex coordinates: A[18; 0] B[0; 0] C[7.08333333333; 7.05987809775]
Centroid: CG[8.36111111111; 2.35329269925]
Coordinates of the circumscribed circle: U[9; -1.94879284091]
Coordinates of the inscribed circle: I[7.5; 3.09989770145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.113305323° = 147°6'47″ = 0.57439855021 rad
∠ B' = β' = 135.0999472039° = 135°5'58″ = 0.78436620488 rad
∠ C' = γ' = 77.78774747311° = 77°47'15″ = 1.78439451027 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 = 10 ; ; b = 13 ; ; c = 18 ; ;

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

p = a+b+c = 10+13+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-10)(20.5-13)(20.5-18) } ; ; T = sqrt{ 4035.94 } = 63.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.53 }{ 10 } = 12.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.53 }{ 13 } = 9.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.53 }{ 18 } = 7.06 ; ;

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{ 10**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 32° 53'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 44° 54'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-13**2 }{ 2 * 13 * 10 } ) = 102° 12'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.53 }{ 20.5 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 32° 53'13" } = 9.21 ; ;




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