Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.62   b = 1.41   c = 6.32

Area: T = 1.89330004713
Perimeter: p = 15.35
Semiperimeter: s = 7.675

Angle ∠ A = α = 154.8588279412° = 154°51'30″ = 2.70327868497 rad
Angle ∠ B = β = 4.50989941394° = 4°30'32″ = 0.07986967937 rad
Angle ∠ C = γ = 20.63327264489° = 20°37'58″ = 0.36601090102 rad

Height: ha = 0.49768505174
Height: hb = 2.68551070515
Height: hc = 0.59990507821

Median: ma = 2.54395176707
Median: mb = 6.96546518219
Median: mc = 4.47766784562

Inradius: r = 0.24766450125
Circumradius: R = 8.96876871492

Vertex coordinates: A[6.32; 0] B[0; 0] C[7.59664161392; 0.59990507821]
Centroid: CG[4.63988053797; 0.2199683594]
Coordinates of the circumscribed circle: U[3.16; 8.39224854963]
Coordinates of the inscribed circle: I[6.265; 0.24766450125]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 25.14217205882° = 25°8'30″ = 2.70327868497 rad
∠ B' = β' = 175.4911005861° = 175°29'28″ = 0.07986967937 rad
∠ C' = γ' = 159.3677273551° = 159°22'2″ = 0.36601090102 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 = 7.62+1.41+6.32 = 15.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.35 }{ 2 } = 7.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.68 * (7.68-7.62)(7.68-1.41)(7.68-6.32) } ; ; T = sqrt{ 3.58 } = 1.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.89 }{ 7.62 } = 0.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.89 }{ 1.41 } = 2.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.89 }{ 6.32 } = 0.6 ; ;

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{ 1.41**2+6.32**2-7.62**2 }{ 2 * 1.41 * 6.32 } ) = 154° 51'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.62**2+6.32**2-1.41**2 }{ 2 * 7.62 * 6.32 } ) = 4° 30'32" ; ;
 gamma = 180° - alpha - beta = 180° - 154° 51'30" - 4° 30'32" = 20° 37'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.89 }{ 7.68 } = 0.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.62 }{ 2 * sin 154° 51'30" } = 8.97 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 6.32**2 - 7.62**2 } }{ 2 } = 2.54 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 7.62**2 - 1.41**2 } }{ 2 } = 6.965 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 7.62**2 - 6.32**2 } }{ 2 } = 4.477 ; ;
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