Triangle calculator SSS - result

Please enter the triangle sides:


Right isosceles triangle.

Sides: a = 2602   b = 2602   c = 3679.78

Area: T = 33852021.99999
Perimeter: p = 8883.78
Semiperimeter: s = 4441.89

Angle ∠ A = α = 455.0000574438° = 45° = 0.7855399166 rad
Angle ∠ B = β = 455.0000574438° = 45° = 0.7855399166 rad
Angle ∠ C = γ = 909.9998851123° = 90° = 1.57107943216 rad

Height: ha = 26021.99999999
Height: hb = 26021.99999999
Height: hc = 1839.894368929

Median: ma = 2909.122210541
Median: mb = 2909.122210541
Median: mc = 1839.894368929

Inradius: r = 762.1088471843
Circumradius: R = 1839.89

Vertex coordinates: A[3679.78; 0] B[0; 0] C[1839.89; 1839.894368929]
Centroid: CG[1839.89; 613.2987896431]
Coordinates of the circumscribed circle: U[1839.89; 0.00436892892]
Coordinates of the inscribed circle: I[1839.89; 762.1088471843]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1354.999942556° = 135° = 0.7855399166 rad
∠ B' = β' = 1354.999942556° = 135° = 0.7855399166 rad
∠ C' = γ' = 900.0001148877° = 90° = 1.57107943216 rad

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How did we calculate this triangle?

a = 2602 ; ; b = 2602 ; ; c = 3679.78 ; ;

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

p = a+b+c = 2602+2602+3679.78 = 8883.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8883.78 }{ 2 } = 4441.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4441.89 * (4441.89-2602)(4441.89-2602)(4441.89-3679.78) } ; ; T = sqrt{ 1.146 * 10**{ 13 } } = 3385202 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3385202 }{ 2602 } = 2602 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3385202 }{ 2602 } = 2602 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3385202 }{ 3679.78 } = 1839.89 ; ;

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{ 2602**2+3679.78**2-2602**2 }{ 2 * 2602 * 3679.78 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2602**2+3679.78**2-2602**2 }{ 2 * 2602 * 3679.78 } ) = 45° ; ; gamma = 180° - alpha - beta = 180° - 45° - 45° = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3385202 }{ 4441.89 } = 762.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2602 }{ 2 * sin 45° } = 1839.89 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2602**2+2 * 3679.78**2 - 2602**2 } }{ 2 } = 2909.122 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3679.78**2+2 * 2602**2 - 2602**2 } }{ 2 } = 2909.122 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2602**2+2 * 2602**2 - 3679.78**2 } }{ 2 } = 1839.894 ; ;
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