10 14 18 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 14   c = 18

Area: T = 69.64991205975
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 50.70435197608° = 50°42'13″ = 0.88549433622 rad
Angle ∠ C = γ = 95.73991704773° = 95°44'21″ = 1.6710963748 rad

Height: ha = 13.93298241195
Height: hb = 9.95498743711
Height: hc = 7.73987911775

Median: ma = 15.33297097168
Median: mb = 12.76771453348
Median: mc = 8.18553527719

Inradius: r = 3.31766247904
Circumradius: R = 9.04553403373

Vertex coordinates: A[18; 0] B[0; 0] C[6.33333333333; 7.73987911775]
Centroid: CG[8.11111111111; 2.58795970592]
Coordinates of the circumscribed circle: U[9; -0.90545340337]
Coordinates of the inscribed circle: I[7; 3.31766247904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 129.2966480239° = 129°17'47″ = 0.88549433622 rad
∠ C' = γ' = 84.26108295227° = 84°15'39″ = 1.6710963748 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 = 14 ; ; c = 18 ; ;

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

p = a+b+c = 10+14+18 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-10)(21-14)(21-18) } ; ; T = sqrt{ 4851 } = 69.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.65 }{ 10 } = 13.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.65 }{ 14 } = 9.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.65 }{ 18 } = 7.74 ; ;

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**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 33° 33'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 50° 42'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-14**2 }{ 2 * 14 * 10 } ) = 95° 44'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.65 }{ 21 } = 3.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 33° 33'26" } = 9.05 ; ;




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