Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.39   b = 3.32   c = 2.45

Area: T = 2.73985475639
Perimeter: p = 11.16
Semiperimeter: s = 5.58

Angle ∠ A = α = 137.6733220065° = 137°40'24″ = 2.4032850982 rad
Angle ∠ B = β = 24.50441173744° = 24°30'15″ = 0.42876775285 rad
Angle ∠ C = γ = 17.82326625605° = 17°49'22″ = 0.31110641432 rad

Height: ha = 1.01661586508
Height: hb = 1.65497274482
Height: hc = 2.23655490318

Median: ma = 1.11877768114
Median: mb = 3.8433396935
Median: mc = 4.30554180982

Inradius: r = 0.49107791333
Circumradius: R = 4.00223277829

Vertex coordinates: A[2.45; 0] B[0; 0] C[4.90545306122; 2.23655490318]
Centroid: CG[2.45215102041; 0.74551830106]
Coordinates of the circumscribed circle: U[1.225; 3.81102496876]
Coordinates of the inscribed circle: I[2.26; 0.49107791333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.32767799349° = 42°19'36″ = 2.4032850982 rad
∠ B' = β' = 155.4965882626° = 155°29'45″ = 0.42876775285 rad
∠ C' = γ' = 162.1777337439° = 162°10'38″ = 0.31110641432 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 = 5.39+3.32+2.45 = 11.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.16 }{ 2 } = 5.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.58 * (5.58-5.39)(5.58-3.32)(5.58-2.45) } ; ; T = sqrt{ 7.5 } = 2.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.74 }{ 5.39 } = 1.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.74 }{ 3.32 } = 1.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.74 }{ 2.45 } = 2.24 ; ;

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{ 3.32**2+2.45**2-5.39**2 }{ 2 * 3.32 * 2.45 } ) = 137° 40'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.39**2+2.45**2-3.32**2 }{ 2 * 5.39 * 2.45 } ) = 24° 30'15" ; ;
 gamma = 180° - alpha - beta = 180° - 137° 40'24" - 24° 30'15" = 17° 49'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.74 }{ 5.58 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.39 }{ 2 * sin 137° 40'24" } = 4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.32**2+2 * 2.45**2 - 5.39**2 } }{ 2 } = 1.118 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.45**2+2 * 5.39**2 - 3.32**2 } }{ 2 } = 3.843 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.32**2+2 * 5.39**2 - 2.45**2 } }{ 2 } = 4.305 ; ;
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