Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 4.24   b = 4.12   c = 4.12

Area: T = 7.48993332146
Perimeter: p = 12.48
Semiperimeter: s = 6.24

Angle ∠ A = α = 61.9376513815° = 61°56'11″ = 1.08109960933 rad
Angle ∠ B = β = 59.03217430925° = 59°1'54″ = 1.03302982802 rad
Angle ∠ C = γ = 59.03217430925° = 59°1'54″ = 1.03302982802 rad

Height: ha = 3.53327043465
Height: hb = 3.63655986479
Height: hc = 3.63655986479

Median: ma = 3.53327043465
Median: mb = 3.63876365954
Median: mc = 3.63876365954

Inradius: r = 1.22002136562
Circumradius: R = 2.4022465411

Vertex coordinates: A[4.12; 0] B[0; 0] C[2.18217475728; 3.63655986479]
Centroid: CG[2.10105825243; 1.2121866216]
Coordinates of the circumscribed circle: U[2.06; 1.23662200659]
Coordinates of the inscribed circle: I[2.12; 1.22002136562]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.0633486185° = 118°3'49″ = 1.08109960933 rad
∠ B' = β' = 120.9688256908° = 120°58'6″ = 1.03302982802 rad
∠ C' = γ' = 120.9688256908° = 120°58'6″ = 1.03302982802 rad

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How did we calculate this triangle?

a = 4.24 ; ; b = 4.12 ; ; c = 4.12 ; ;

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

p = a+b+c = 4.24+4.12+4.12 = 12.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.48 }{ 2 } = 6.24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.24 * (6.24-4.24)(6.24-4.12)(6.24-4.12) } ; ; T = sqrt{ 56.09 } = 7.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.49 }{ 4.24 } = 3.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.49 }{ 4.12 } = 3.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.49 }{ 4.12 } = 3.64 ; ;

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{ 4.12**2+4.12**2-4.24**2 }{ 2 * 4.12 * 4.12 } ) = 61° 56'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.24**2+4.12**2-4.12**2 }{ 2 * 4.24 * 4.12 } ) = 59° 1'54" ; ; gamma = 180° - alpha - beta = 180° - 61° 56'11" - 59° 1'54" = 59° 1'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.49 }{ 6.24 } = 1.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.24 }{ 2 * sin 61° 56'11" } = 2.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.12**2+2 * 4.12**2 - 4.24**2 } }{ 2 } = 3.533 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.12**2+2 * 4.24**2 - 4.12**2 } }{ 2 } = 3.638 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.12**2+2 * 4.24**2 - 4.12**2 } }{ 2 } = 3.638 ; ;
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