Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 4.12   b = 5.1   c = 6.4

Area: T = 10.49438028755
Perimeter: p = 15.62
Semiperimeter: s = 7.81

Angle ∠ A = α = 40.01660839832° = 40°58″ = 0.69884124193 rad
Angle ∠ B = β = 52.74550640182° = 52°44'42″ = 0.92105750313 rad
Angle ∠ C = γ = 87.23988519986° = 87°14'20″ = 1.5232605203 rad

Height: ha = 5.09440790658
Height: hb = 4.11552168139
Height: hc = 3.27993133986

Median: ma = 5.40875317845
Median: mb = 4.7439694083
Median: mc = 3.35444299069

Inradius: r = 1.34436367318
Circumradius: R = 3.20437194141

Vertex coordinates: A[6.4; 0] B[0; 0] C[2.494409375; 3.27993133986]
Centroid: CG[2.96546979167; 1.09331044662]
Coordinates of the circumscribed circle: U[3.2; 0.15443310866]
Coordinates of the inscribed circle: I[2.71; 1.34436367318]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9843916017° = 139°59'2″ = 0.69884124193 rad
∠ B' = β' = 127.2554935982° = 127°15'18″ = 0.92105750313 rad
∠ C' = γ' = 92.76111480014° = 92°45'40″ = 1.5232605203 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 = 4.12+5.1+6.4 = 15.62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.62 }{ 2 } = 7.81 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.81 * (7.81-4.12)(7.81-5.1)(7.81-6.4) } ; ; T = sqrt{ 110.12 } = 10.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.49 }{ 4.12 } = 5.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.49 }{ 5.1 } = 4.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.49 }{ 6.4 } = 3.28 ; ;

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{ 5.1**2+6.4**2-4.12**2 }{ 2 * 5.1 * 6.4 } ) = 40° 58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.12**2+6.4**2-5.1**2 }{ 2 * 4.12 * 6.4 } ) = 52° 44'42" ; ; gamma = 180° - alpha - beta = 180° - 40° 58" - 52° 44'42" = 87° 14'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.49 }{ 7.81 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.12 }{ 2 * sin 40° 58" } = 3.2 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 6.4**2 - 4.12**2 } }{ 2 } = 5.408 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 4.12**2 - 5.1**2 } }{ 2 } = 4.74 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 4.12**2 - 6.4**2 } }{ 2 } = 3.354 ; ;
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