9.49 3.61 12.04 triangle

Obtuse scalene triangle.

Sides: a = 9.49   b = 3.61   c = 12.04

Area: T = 13.55992271638
Perimeter: p = 25.14
Semiperimeter: s = 12.57

Angle ∠ A = α = 38.60332082282° = 38°36'12″ = 0.67437530854 rad
Angle ∠ B = β = 13.73296397558° = 13°43'47″ = 0.24396274189 rad
Angle ∠ C = γ = 127.6677152016° = 127°40'2″ = 2.22882121493 rad

Height: ha = 2.85875821209
Height: hb = 7.51220372099
Height: hc = 2.25223633162

Median: ma = 7.51554391089
Median: mb = 10.68989113103
Median: mc = 3.9122249992

Inradius: r = 1.07986974673
Circumradius: R = 7.60551007741

Vertex coordinates: A[12.04; 0] B[0; 0] C[9.21988372093; 2.25223633162]
Centroid: CG[7.08662790698; 0.75107877721]
Coordinates of the circumscribed circle: U[6.02; -4.64772742317]
Coordinates of the inscribed circle: I[8.96; 1.07986974673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3976791772° = 141°23'48″ = 0.67437530854 rad
∠ B' = β' = 166.2770360244° = 166°16'13″ = 0.24396274189 rad
∠ C' = γ' = 52.3332847984° = 52°19'58″ = 2.22882121493 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 = 9.49+3.61+12.04 = 25.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.14 }{ 2 } = 12.57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.57 * (12.57-9.49)(12.57-3.61)(12.57-12.04) } ; ; T = sqrt{ 183.85 } = 13.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.56 }{ 9.49 } = 2.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.56 }{ 3.61 } = 7.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.56 }{ 12.04 } = 2.25 ; ;

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{ 3.61**2+12.04**2-9.49**2 }{ 2 * 3.61 * 12.04 } ) = 38° 36'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.49**2+12.04**2-3.61**2 }{ 2 * 9.49 * 12.04 } ) = 13° 43'47" ; ;
 gamma = 180° - alpha - beta = 180° - 38° 36'12" - 13° 43'47" = 127° 40'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.56 }{ 12.57 } = 1.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.49 }{ 2 * sin 38° 36'12" } = 7.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.61**2+2 * 12.04**2 - 9.49**2 } }{ 2 } = 7.515 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.04**2+2 * 9.49**2 - 3.61**2 } }{ 2 } = 10.689 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.61**2+2 * 9.49**2 - 12.04**2 } }{ 2 } = 3.912 ; ;
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