Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 4   b = 9   c = 6

Area: T = 9.56222957495
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 20.74219164807° = 20°44'31″ = 0.36220147358 rad
Angle ∠ B = β = 127.1698899656° = 127°10'8″ = 2.22195160051 rad
Angle ∠ C = γ = 32.08991838633° = 32°5'21″ = 0.56600619127 rad

Height: ha = 4.78111478747
Height: hb = 2.1254954611
Height: hc = 3.18774319165

Median: ma = 7.38224115301
Median: mb = 2.39879157617
Median: mc = 6.2854902545

Inradius: r = 1.00765574473
Circumradius: R = 5.64771794447

Vertex coordinates: A[6; 0] B[0; 0] C[-2.41766666667; 3.18774319165]
Centroid: CG[1.19444444444; 1.06224773055]
Coordinates of the circumscribed circle: U[3; 4.78444159184]
Coordinates of the inscribed circle: I[0.5; 1.00765574473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.2588083519° = 159°15'29″ = 0.36220147358 rad
∠ B' = β' = 52.8311100344° = 52°49'52″ = 2.22195160051 rad
∠ C' = γ' = 147.9110816137° = 147°54'39″ = 0.56600619127 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+9+6 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-4)(9.5-9)(9.5-6) } ; ; T = sqrt{ 91.44 } = 9.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.56 }{ 4 } = 4.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.56 }{ 9 } = 2.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.56 }{ 6 } = 3.19 ; ;

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{ 9**2+6**2-4**2 }{ 2 * 9 * 6 } ) = 20° 44'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+6**2-9**2 }{ 2 * 4 * 6 } ) = 127° 10'8" ; ; gamma = 180° - alpha - beta = 180° - 20° 44'31" - 127° 10'8" = 32° 5'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.56 }{ 9.5 } = 1.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 20° 44'31" } = 5.65 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9**2+2 * 6**2 - 4**2 } }{ 2 } = 7.382 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 4**2 - 9**2 } }{ 2 } = 2.398 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9**2+2 * 4**2 - 6**2 } }{ 2 } = 6.285 ; ;
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