8.6 8.25 7.07 triangle

Acute scalene triangle.

Sides: a = 8.6   b = 8.25   c = 7.07

Area: T = 27.00107988148
Perimeter: p = 23.92
Semiperimeter: s = 11.96

Angle ∠ A = α = 67.79444919112° = 67°47'40″ = 1.18332370986 rad
Angle ∠ B = β = 62.64223073688° = 62°38'32″ = 1.09333145146 rad
Angle ∠ C = γ = 49.563320072° = 49°33'48″ = 0.86550410404 rad

Height: ha = 6.27992555383
Height: hb = 6.54656481975
Height: hc = 7.63881326209

Median: ma = 6.36766082022
Median: mb = 6.70549850857
Median: mc = 7.65495114223

Inradius: r = 2.25875918742
Circumradius: R = 4.64444598125

Vertex coordinates: A[7.07; 0] B[0; 0] C[3.95220792079; 7.63881326209]
Centroid: CG[3.67440264026; 2.5466044207]
Coordinates of the circumscribed circle: U[3.535; 3.01224378748]
Coordinates of the inscribed circle: I[3.71; 2.25875918742]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.2065508089° = 112°12'20″ = 1.18332370986 rad
∠ B' = β' = 117.3587692631° = 117°21'28″ = 1.09333145146 rad
∠ C' = γ' = 130.437679928° = 130°26'12″ = 0.86550410404 rad

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How did we calculate this triangle?

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

p = a+b+c = 8.6+8.25+7.07 = 23.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.92 }{ 2 } = 11.96 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.96 * (11.96-8.6)(11.96-8.25)(11.96-7.07) } ; ; T = sqrt{ 729.04 } = 27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27 }{ 8.6 } = 6.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27 }{ 8.25 } = 6.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27 }{ 7.07 } = 7.64 ; ;

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{ 8.25**2+7.07**2-8.6**2 }{ 2 * 8.25 * 7.07 } ) = 67° 47'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.6**2+7.07**2-8.25**2 }{ 2 * 8.6 * 7.07 } ) = 62° 38'32" ; ;
 gamma = 180° - alpha - beta = 180° - 67° 47'40" - 62° 38'32" = 49° 33'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27 }{ 11.96 } = 2.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.6 }{ 2 * sin 67° 47'40" } = 4.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.25**2+2 * 7.07**2 - 8.6**2 } }{ 2 } = 6.367 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 8.6**2 - 8.25**2 } }{ 2 } = 6.705 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.25**2+2 * 8.6**2 - 7.07**2 } }{ 2 } = 7.65 ; ;
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