7.88 9.41 11.47 triangle

Acute scalene triangle.

Sides: a = 7.88   b = 9.41   c = 11.47

Area: T = 36.76772213935
Perimeter: p = 28.76
Semiperimeter: s = 14.38

Angle ∠ A = α = 42.94552366699° = 42°56'43″ = 0.75495357779 rad
Angle ∠ B = β = 54.44773638692° = 54°26'50″ = 0.95502857685 rad
Angle ∠ C = γ = 82.60773994609° = 82°36'27″ = 1.44217711071 rad

Height: ha = 9.33217820796
Height: hb = 7.81444997648
Height: hc = 6.41110237827

Median: ma = 9.72327002422
Median: mb = 8.64223738058
Median: mc = 6.51439101161

Inradius: r = 2.55768304168
Circumradius: R = 5.78330701081

Vertex coordinates: A[11.47; 0] B[0; 0] C[4.58218308631; 6.41110237827]
Centroid: CG[5.35106102877; 2.13770079276]
Coordinates of the circumscribed circle: U[5.735; 0.74440933245]
Coordinates of the inscribed circle: I[4.97; 2.55768304168]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.055476333° = 137°3'17″ = 0.75495357779 rad
∠ B' = β' = 125.5532636131° = 125°33'10″ = 0.95502857685 rad
∠ C' = γ' = 97.39326005391° = 97°23'33″ = 1.44217711071 rad

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How did we calculate this triangle?

a = 7.88 ; ; b = 9.41 ; ; c = 11.47 ; ;

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

p = a+b+c = 7.88+9.41+11.47 = 28.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28.76 }{ 2 } = 14.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.38 * (14.38-7.88)(14.38-9.41)(14.38-11.47) } ; ; T = sqrt{ 1351.83 } = 36.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.77 }{ 7.88 } = 9.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.77 }{ 9.41 } = 7.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.77 }{ 11.47 } = 6.41 ; ;

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{ 7.88**2-9.41**2-11.47**2 }{ 2 * 9.41 * 11.47 } ) = 42° 56'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.41**2-7.88**2-11.47**2 }{ 2 * 7.88 * 11.47 } ) = 54° 26'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.47**2-7.88**2-9.41**2 }{ 2 * 9.41 * 7.88 } ) = 82° 36'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.77 }{ 14.38 } = 2.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.88 }{ 2 * sin 42° 56'43" } = 5.78 ; ;




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