Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 5.1   b = 4.1   c = 6.37

Area: T = 10.4439950019
Perimeter: p = 15.57
Semiperimeter: s = 7.785

Angle ∠ A = α = 53.08800396154° = 53°4'48″ = 0.92664214584 rad
Angle ∠ B = β = 39.99546104766° = 39°59'41″ = 0.69880376359 rad
Angle ∠ C = γ = 86.9255349908° = 86°55'31″ = 1.51771335593 rad

Height: ha = 4.09440980467
Height: hb = 5.09326585459
Height: hc = 3.27878492995

Median: ma = 4.71107271201
Median: mb = 5.39436026921
Median: mc = 3.35664527406

Inradius: r = 1.34110340423
Circumradius: R = 3.19895914194

Vertex coordinates: A[6.37; 0] B[0; 0] C[3.90771350078; 3.27878492995]
Centroid: CG[3.42657116693; 1.09326164332]
Coordinates of the circumscribed circle: U[3.185; 0.17110801653]
Coordinates of the inscribed circle: I[3.685; 1.34110340423]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.9219960385° = 126°55'12″ = 0.92664214584 rad
∠ B' = β' = 140.0055389523° = 140°19″ = 0.69880376359 rad
∠ C' = γ' = 93.0754650092° = 93°4'29″ = 1.51771335593 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 = 5.1+4.1+6.37 = 15.57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.57 }{ 2 } = 7.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.79 * (7.79-5.1)(7.79-4.1)(7.79-6.37) } ; ; T = sqrt{ 108.99 } = 10.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.44 }{ 5.1 } = 4.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.44 }{ 4.1 } = 5.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.44 }{ 6.37 } = 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{ 4.1**2+6.37**2-5.1**2 }{ 2 * 4.1 * 6.37 } ) = 53° 4'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.1**2+6.37**2-4.1**2 }{ 2 * 5.1 * 6.37 } ) = 39° 59'41" ; ;
 gamma = 180° - alpha - beta = 180° - 53° 4'48" - 39° 59'41" = 86° 55'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.44 }{ 7.79 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.1 }{ 2 * sin 53° 4'48" } = 3.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.1**2+2 * 6.37**2 - 5.1**2 } }{ 2 } = 4.711 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.37**2+2 * 5.1**2 - 4.1**2 } }{ 2 } = 5.394 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.1**2+2 * 5.1**2 - 6.37**2 } }{ 2 } = 3.356 ; ;
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