Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.4   b = 3.59   c = 4.8

Area: T = 6.09328390262
Perimeter: p = 11.79
Semiperimeter: s = 5.895

Angle ∠ A = α = 45.00438277215° = 45°14″ = 0.78554649697 rad
Angle ∠ B = β = 48.30328653421° = 48°18'10″ = 0.84330440384 rad
Angle ∠ C = γ = 86.69333069364° = 86°41'36″ = 1.51330836455 rad

Height: ha = 3.58440229566
Height: hb = 3.39443392904
Height: hc = 2.53986829276

Median: ma = 3.88325313907
Median: mb = 3.7522062766
Median: mc = 2.54224496062

Inradius: r = 1.03435604794
Circumradius: R = 2.40440024588

Vertex coordinates: A[4.8; 0] B[0; 0] C[2.262165625; 2.53986829276]
Centroid: CG[2.35438854167; 0.84662276425]
Coordinates of the circumscribed circle: U[2.4; 0.13986644217]
Coordinates of the inscribed circle: I[2.305; 1.03435604794]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9966172278° = 134°59'46″ = 0.78554649697 rad
∠ B' = β' = 131.6977134658° = 131°41'50″ = 0.84330440384 rad
∠ C' = γ' = 93.30766930636° = 93°18'24″ = 1.51330836455 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 = 3.4+3.59+4.8 = 11.79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.79 }{ 2 } = 5.9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.9 * (5.9-3.4)(5.9-3.59)(5.9-4.8) } ; ; T = sqrt{ 37.12 } = 6.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.09 }{ 3.4 } = 3.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.09 }{ 3.59 } = 3.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.09 }{ 4.8 } = 2.54 ; ;

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{ 3.59**2+4.8**2-3.4**2 }{ 2 * 3.59 * 4.8 } ) = 45° 14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.4**2+4.8**2-3.59**2 }{ 2 * 3.4 * 4.8 } ) = 48° 18'10" ; ;
 gamma = 180° - alpha - beta = 180° - 45° 14" - 48° 18'10" = 86° 41'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.09 }{ 5.9 } = 1.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.4 }{ 2 * sin 45° 14" } = 2.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.59**2+2 * 4.8**2 - 3.4**2 } }{ 2 } = 3.883 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.8**2+2 * 3.4**2 - 3.59**2 } }{ 2 } = 3.752 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.59**2+2 * 3.4**2 - 4.8**2 } }{ 2 } = 2.542 ; ;
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