8.94 7.5 14.99 triangle

Obtuse scalene triangle.

Sides: a = 8.94   b = 7.5   c = 14.99

Area: T = 25.18216758747
Perimeter: p = 31.43
Semiperimeter: s = 15.715

Angle ∠ A = α = 26.61437006416° = 26°36'49″ = 0.46444967023 rad
Angle ∠ B = β = 22.07547667147° = 22°4'29″ = 0.38552773608 rad
Angle ∠ C = γ = 131.3121532644° = 131°18'42″ = 2.29218185905 rad

Height: ha = 5.63334845357
Height: hb = 6.71551135666
Height: hc = 3.36597966477

Median: ma = 10.97769827366
Median: mb = 11.75879483755
Median: mc = 3.45113439411

Inradius: r = 1.60223974467
Circumradius: R = 9.97882824721

Vertex coordinates: A[14.99; 0] B[0; 0] C[8.2854646431; 3.36597966477]
Centroid: CG[7.7588215477; 1.12199322159]
Coordinates of the circumscribed circle: U[7.495; -6.58771918216]
Coordinates of the inscribed circle: I[8.215; 1.60223974467]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3866299358° = 153°23'11″ = 0.46444967023 rad
∠ B' = β' = 157.9255233285° = 157°55'31″ = 0.38552773608 rad
∠ C' = γ' = 48.68884673562° = 48°41'18″ = 2.29218185905 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 = 8.94 ; ; b = 7.5 ; ; c = 14.99 ; ;

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

p = a+b+c = 8.94+7.5+14.99 = 31.43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.43 }{ 2 } = 15.72 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.72 * (15.72-8.94)(15.72-7.5)(15.72-14.99) } ; ; T = sqrt{ 634.12 } = 25.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.18 }{ 8.94 } = 5.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.18 }{ 7.5 } = 6.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.18 }{ 14.99 } = 3.36 ; ;

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{ 7.5**2+14.99**2-8.94**2 }{ 2 * 7.5 * 14.99 } ) = 26° 36'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.94**2+14.99**2-7.5**2 }{ 2 * 8.94 * 14.99 } ) = 22° 4'29" ; ;
 gamma = 180° - alpha - beta = 180° - 26° 36'49" - 22° 4'29" = 131° 18'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.18 }{ 15.72 } = 1.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.94 }{ 2 * sin 26° 36'49" } = 9.98 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.5**2+2 * 14.99**2 - 8.94**2 } }{ 2 } = 10.977 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.99**2+2 * 8.94**2 - 7.5**2 } }{ 2 } = 11.758 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.5**2+2 * 8.94**2 - 14.99**2 } }{ 2 } = 3.451 ; ;
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