Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 0.34   b = 0.37   c = 0.13

Area: T = 0.02220726075
Perimeter: p = 0.84
Semiperimeter: s = 0.42

Angle ∠ A = α = 66.60436517245° = 66°36'13″ = 1.16224530164 rad
Angle ∠ B = β = 92.8533004976° = 92°51'11″ = 1.62105906572 rad
Angle ∠ C = γ = 20.54333432994° = 20°32'36″ = 0.35985489799 rad

Height: ha = 0.13298388674
Height: hb = 0.11993113917
Height: hc = 0.34395785763

Median: ma = 0.2199089023
Median: mb = 0.17989553017
Median: mc = 0.34993207695

Inradius: r = 0.05325538273
Circumradius: R = 0.18552295887

Vertex coordinates: A[0.13; 0] B[0; 0] C[-0.01769230769; 0.34395785763]
Centroid: CG[0.03876923077; 0.11331928588]
Coordinates of the circumscribed circle: U[0.065; 0.17334502825]
Coordinates of the inscribed circle: I[0.05; 0.05325538273]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 113.3966348275° = 113°23'47″ = 1.16224530164 rad
∠ B' = β' = 87.1476995024° = 87°8'49″ = 1.62105906572 rad
∠ C' = γ' = 159.4576656701° = 159°27'24″ = 0.35985489799 rad

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How did we calculate this triangle?

a = 0.34 ; ; b = 0.37 ; ; c = 0.13 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 0.34+0.37+0.13 = 0.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.84 }{ 2 } = 0.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.42 * (0.42-0.34)(0.42-0.37)(0.42-0.13) } ; ; T = sqrt{ 0 } = 0.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.02 }{ 0.34 } = 0.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.02 }{ 0.37 } = 0.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.02 }{ 0.13 } = 0.34 ; ;

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{ 0.37**2+0.13**2-0.34**2 }{ 2 * 0.37 * 0.13 } ) = 66° 36'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.34**2+0.13**2-0.37**2 }{ 2 * 0.34 * 0.13 } ) = 92° 51'11" ; ; gamma = 180° - alpha - beta = 180° - 66° 36'13" - 92° 51'11" = 20° 32'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.02 }{ 0.42 } = 0.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.34 }{ 2 * sin 66° 36'13" } = 0.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.37**2+2 * 0.13**2 - 0.34**2 } }{ 2 } = 0.219 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.13**2+2 * 0.34**2 - 0.37**2 } }{ 2 } = 0.179 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.37**2+2 * 0.34**2 - 0.13**2 } }{ 2 } = 0.349 ; ;
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