Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.09   b = 1.78   c = 3.57

Area: T = 2.75500908349
Perimeter: p = 8.44
Semiperimeter: s = 4.22

Angle ∠ A = α = 59.94548049019° = 59°56'41″ = 1.0466234215 rad
Angle ∠ B = β = 29.90772730274° = 29°54'26″ = 0.52219803846 rad
Angle ∠ C = γ = 90.14879220706° = 90°8'53″ = 1.5733378054 rad

Height: ha = 1.78799940679
Height: hb = 3.09899897021
Height: hc = 1.54106671344

Median: ma = 2.36600052966
Median: mb = 3.21878253526
Median: mc = 1.78110179673

Inradius: r = 0.65216802926
Circumradius: R = 1.78550059488

Vertex coordinates: A[3.57; 0] B[0; 0] C[2.67985154062; 1.54106671344]
Centroid: CG[2.08328384687; 0.51435557115]
Coordinates of the circumscribed circle: U[1.785; -0.00546083932]
Coordinates of the inscribed circle: I[2.44; 0.65216802926]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.0555195098° = 120°3'19″ = 1.0466234215 rad
∠ B' = β' = 150.0932726973° = 150°5'34″ = 0.52219803846 rad
∠ C' = γ' = 89.85220779294° = 89°51'7″ = 1.5733378054 rad

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How did we calculate this triangle?

a = 3.09 ; ; b = 1.78 ; ; c = 3.57 ; ;

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

p = a+b+c = 3.09+1.78+3.57 = 8.44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.44 }{ 2 } = 4.22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.22 * (4.22-3.09)(4.22-1.78)(4.22-3.57) } ; ; T = sqrt{ 7.56 } = 2.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.75 }{ 3.09 } = 1.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.75 }{ 1.78 } = 3.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.75 }{ 3.57 } = 1.54 ; ;

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{ 1.78**2+3.57**2-3.09**2 }{ 2 * 1.78 * 3.57 } ) = 59° 56'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.09**2+3.57**2-1.78**2 }{ 2 * 3.09 * 3.57 } ) = 29° 54'26" ; ; gamma = 180° - alpha - beta = 180° - 59° 56'41" - 29° 54'26" = 90° 8'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.75 }{ 4.22 } = 0.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.09 }{ 2 * sin 59° 56'41" } = 1.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.78**2+2 * 3.57**2 - 3.09**2 } }{ 2 } = 2.36 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.57**2+2 * 3.09**2 - 1.78**2 } }{ 2 } = 3.218 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.78**2+2 * 3.09**2 - 3.57**2 } }{ 2 } = 1.781 ; ;
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