8 9 14 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 9   c = 14

Area: T = 33.66765635312
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 32.30325452092° = 32°18'9″ = 0.56437857707 rad
Angle ∠ B = β = 36.95550748363° = 36°57'18″ = 0.64549877312 rad
Angle ∠ C = γ = 110.7422379954° = 110°44'33″ = 1.93328191517 rad

Height: ha = 8.41766408828
Height: hb = 7.48114585625
Height: hc = 4.81095090759

Median: ma = 11.06879718106
Median: mb = 10.47661634199
Median: mc = 4.84876798574

Inradius: r = 2.17220363569
Circumradius: R = 7.48551714451

Vertex coordinates: A[14; 0] B[0; 0] C[6.39328571429; 4.81095090759]
Centroid: CG[6.79876190476; 1.6033169692]
Coordinates of the circumscribed circle: U[7; -2.65109982202]
Coordinates of the inscribed circle: I[6.5; 2.17220363569]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.6977454791° = 147°41'51″ = 0.56437857707 rad
∠ B' = β' = 143.0454925164° = 143°2'42″ = 0.64549877312 rad
∠ C' = γ' = 69.25876200455° = 69°15'27″ = 1.93328191517 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 = 8 ; ; b = 9 ; ; c = 14 ; ;

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

p = a+b+c = 8+9+14 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-8)(15.5-9)(15.5-14) } ; ; T = sqrt{ 1133.44 } = 33.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.67 }{ 8 } = 8.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.67 }{ 9 } = 7.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.67 }{ 14 } = 4.81 ; ;

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{ 8**2-9**2-14**2 }{ 2 * 9 * 14 } ) = 32° 18'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-8**2-14**2 }{ 2 * 8 * 14 } ) = 36° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-8**2-9**2 }{ 2 * 9 * 8 } ) = 110° 44'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.67 }{ 15.5 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 32° 18'9" } = 7.49 ; ;




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