Triangle calculator SSS - result

Please enter the triangle sides:


Right isosceles triangle.

Sides: a = 342.5   b = 484.37   c = 342.5

Area: T = 58653.12549983
Perimeter: p = 1169.37
Semiperimeter: s = 584.685

Angle ∠ A = α = 454.9997805855° = 44°59'59″ = 0.78553943339 rad
Angle ∠ B = β = 900.0004388291° = 90°2″ = 1.57108039858 rad
Angle ∠ C = γ = 454.9997805855° = 44°59'59″ = 0.78553943339 rad

Height: ha = 342.549999999
Height: hb = 242.1833145109
Height: hc = 342.549999999

Median: ma = 382.9287814281
Median: mb = 242.1833145109
Median: mc = 382.9287814281

Inradius: r = 100.3165768317
Circumradius: R = 242.1855000007

Vertex coordinates: A[342.5; 0] B[0; 0] C[-0.00326232117; 342.549999999]
Centroid: CG[114.1665792263; 114.1676666663]
Coordinates of the circumscribed circle: U[171.25; 171.2511311611]
Coordinates of the inscribed circle: I[100.315; 100.3165768317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1355.000219415° = 135°1″ = 0.78553943339 rad
∠ B' = β' = 909.9995611709° = 89°59'58″ = 1.57108039858 rad
∠ C' = γ' = 1355.000219415° = 135°1″ = 0.78553943339 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 = 342.5+484.37+342.5 = 1169.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1169.37 }{ 2 } = 584.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 584.69 * (584.69-342.5)(584.69-484.37)(584.69-342.5) } ; ; T = sqrt{ 3440189072.06 } = 58653.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58653.12 }{ 342.5 } = 342.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58653.12 }{ 484.37 } = 242.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58653.12 }{ 342.5 } = 342.5 ; ;

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{ 484.37**2+342.5**2-342.5**2 }{ 2 * 484.37 * 342.5 } ) = 44° 59'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 342.5**2+342.5**2-484.37**2 }{ 2 * 342.5 * 342.5 } ) = 90° 2" ; ; gamma = 180° - alpha - beta = 180° - 44° 59'59" - 90° 2" = 44° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58653.12 }{ 584.69 } = 100.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 342.5 }{ 2 * sin 44° 59'59" } = 242.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 484.37**2+2 * 342.5**2 - 342.5**2 } }{ 2 } = 382.928 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 342.5**2+2 * 342.5**2 - 484.37**2 } }{ 2 } = 242.183 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 484.37**2+2 * 342.5**2 - 342.5**2 } }{ 2 } = 382.928 ; ;
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