Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 5.7   b = 4.81   c = 3.33

Area: T = 7.99768953826
Perimeter: p = 13.84
Semiperimeter: s = 6.92

Angle ∠ A = α = 86.89553306377° = 86°53'43″ = 1.51766096242 rad
Angle ∠ B = β = 57.41879433052° = 57°25'5″ = 1.00221321604 rad
Angle ∠ C = γ = 35.6876726057° = 35°41'12″ = 0.6232850869 rad

Height: ha = 2.80659282044
Height: hb = 3.32551124252
Height: hc = 4.80329401697

Median: ma = 2.99883328701
Median: mb = 4.00106780675
Median: mc = 5.00440808347

Inradius: r = 1.156562072
Circumradius: R = 2.85441892082

Vertex coordinates: A[3.33; 0] B[0; 0] C[3.06994894895; 4.80329401697]
Centroid: CG[2.13331631632; 1.60109800566]
Coordinates of the circumscribed circle: U[1.665; 2.3188225838]
Coordinates of the inscribed circle: I[2.11; 1.156562072]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 93.10546693623° = 93°6'17″ = 1.51766096242 rad
∠ B' = β' = 122.5822056695° = 122°34'55″ = 1.00221321604 rad
∠ C' = γ' = 144.3133273943° = 144°18'48″ = 0.6232850869 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 = 5.7+4.81+3.33 = 13.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.84 }{ 2 } = 6.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.92 * (6.92-5.7)(6.92-4.81)(6.92-3.33) } ; ; T = sqrt{ 63.95 } = 8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8 }{ 5.7 } = 2.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8 }{ 4.81 } = 3.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8 }{ 3.33 } = 4.8 ; ;

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{ 4.81**2+3.33**2-5.7**2 }{ 2 * 4.81 * 3.33 } ) = 86° 53'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.7**2+3.33**2-4.81**2 }{ 2 * 5.7 * 3.33 } ) = 57° 25'5" ; ; gamma = 180° - alpha - beta = 180° - 86° 53'43" - 57° 25'5" = 35° 41'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8 }{ 6.92 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.7 }{ 2 * sin 86° 53'43" } = 2.85 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.81**2+2 * 3.33**2 - 5.7**2 } }{ 2 } = 2.998 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.33**2+2 * 5.7**2 - 4.81**2 } }{ 2 } = 4.001 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.81**2+2 * 5.7**2 - 3.33**2 } }{ 2 } = 5.004 ; ;
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