Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 11.04   b = 12.2   c = 11.99

Area: T = 59.39549739528
Perimeter: p = 35.23
Semiperimeter: s = 17.615

Angle ∠ A = α = 54.32999958109° = 54°18' = 0.94877137107 rad
Angle ∠ B = β = 63.82198268995° = 63°49'11″ = 1.11438661074 rad
Angle ∠ C = γ = 61.88801772896° = 61°52'49″ = 1.08800128354 rad

Height: ha = 10.76599590494
Height: hb = 9.73768809759
Height: hc = 9.90774185076

Median: ma = 10.76224184085
Median: mb = 9.77880800774
Median: mc = 9.97109966904

Inradius: r = 3.37218407013
Circumradius: R = 6.79773307021

Vertex coordinates: A[11.99; 0] B[0; 0] C[4.87107964971; 9.90774185076]
Centroid: CG[5.6220265499; 3.30224728359]
Coordinates of the circumscribed circle: U[5.995; 3.20436978125]
Coordinates of the inscribed circle: I[5.415; 3.37218407013]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.7700004189° = 125°42' = 0.94877137107 rad
∠ B' = β' = 116.18801731° = 116°10'49″ = 1.11438661074 rad
∠ C' = γ' = 118.121982271° = 118°7'11″ = 1.08800128354 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 = 11.04+12.2+11.99 = 35.23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.23 }{ 2 } = 17.62 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.62 * (17.62-11.04)(17.62-12.2)(17.62-11.99) } ; ; T = sqrt{ 3527.76 } = 59.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.39 }{ 11.04 } = 10.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.39 }{ 12.2 } = 9.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.39 }{ 11.99 } = 9.91 ; ;

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{ 12.2**2+11.99**2-11.04**2 }{ 2 * 12.2 * 11.99 } ) = 54° 18' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.04**2+11.99**2-12.2**2 }{ 2 * 11.04 * 11.99 } ) = 63° 49'11" ; ; gamma = 180° - alpha - beta = 180° - 54° 18' - 63° 49'11" = 61° 52'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.39 }{ 17.62 } = 3.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.04 }{ 2 * sin 54° 18' } = 6.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.2**2+2 * 11.99**2 - 11.04**2 } }{ 2 } = 10.762 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.99**2+2 * 11.04**2 - 12.2**2 } }{ 2 } = 9.778 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.2**2+2 * 11.04**2 - 11.99**2 } }{ 2 } = 9.971 ; ;
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