Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.3   b = 1.8   c = 3.68

Area: T = 1.64876165786
Perimeter: p = 7.78
Semiperimeter: s = 3.89

Angle ∠ A = α = 29.83326762391° = 29°49'58″ = 0.52106784251 rad
Angle ∠ B = β = 22.91224051877° = 22°54'45″ = 0.43998969101 rad
Angle ∠ C = γ = 127.2554918573° = 127°15'18″ = 2.22110173185 rad

Height: ha = 1.43327100683
Height: hb = 1.83106850873
Height: hc = 0.89554437927

Median: ma = 2.65987026912
Median: mb = 2.93436325605
Median: mc = 0.93877632964

Inradius: r = 0.42435518197
Circumradius: R = 2.31217028862

Vertex coordinates: A[3.68; 0] B[0; 0] C[2.11985326087; 0.89554437927]
Centroid: CG[1.93328442029; 0.29884812642]
Coordinates of the circumscribed circle: U[1.84; -1.39994178196]
Coordinates of the inscribed circle: I[2.09; 0.42435518197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.1677323761° = 150°10'2″ = 0.52106784251 rad
∠ B' = β' = 157.0887594812° = 157°5'15″ = 0.43998969101 rad
∠ C' = γ' = 52.74550814268° = 52°44'42″ = 2.22110173185 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 = 2.3+1.8+3.68 = 7.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.78 }{ 2 } = 3.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.89 * (3.89-2.3)(3.89-1.8)(3.89-3.68) } ; ; T = sqrt{ 2.71 } = 1.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.65 }{ 2.3 } = 1.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.65 }{ 1.8 } = 1.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.65 }{ 3.68 } = 0.9 ; ;

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{ 1.8**2+3.68**2-2.3**2 }{ 2 * 1.8 * 3.68 } ) = 29° 49'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.3**2+3.68**2-1.8**2 }{ 2 * 2.3 * 3.68 } ) = 22° 54'45" ; ; gamma = 180° - alpha - beta = 180° - 29° 49'58" - 22° 54'45" = 127° 15'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.65 }{ 3.89 } = 0.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.3 }{ 2 * sin 29° 49'58" } = 2.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.8**2+2 * 3.68**2 - 2.3**2 } }{ 2 } = 2.659 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.68**2+2 * 2.3**2 - 1.8**2 } }{ 2 } = 2.934 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.8**2+2 * 2.3**2 - 3.68**2 } }{ 2 } = 0.938 ; ;
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