Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 600.63   b = 1415   c = 1537.2

Area: T = 424945.725
Perimeter: p = 3552.83
Semiperimeter: s = 1776.415

Angle ∠ A = α = 232.9999234418° = 23° = 0.40114243918 rad
Angle ∠ B = β = 676.999994207° = 67° = 1.16993704977 rad
Angle ∠ C = γ = 900.0000823513° = 90° = 1.57107977641 rad

Height: ha = 1415
Height: hb = 600.6329999999
Height: hc = 552.8832806401

Median: ma = 1446.518834443
Median: mb = 928.0769969587
Median: mc = 768.5999205341

Inradius: r = 239.2155343824
Circumradius: R = 768.6600000001

Vertex coordinates: A[1537.2; 0] B[0; 0] C[234.6854893605; 552.8832806401]
Centroid: CG[590.6288297868; 184.29442688]
Coordinates of the circumscribed circle: U[768.6; -0.00111047097]
Coordinates of the inscribed circle: I[361.415; 239.2155343824]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1577.000076558° = 157° = 0.40114243918 rad
∠ B' = β' = 1133.000005793° = 113° = 1.16993704977 rad
∠ C' = γ' = 909.9999176487° = 90° = 1.57107977641 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 = 600.63+1415+1537.2 = 3552.83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3552.83 }{ 2 } = 1776.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1776.42 * (1776.42-600.63)(1776.42-1415)(1776.42-1537.2) } ; ; T = sqrt{ 180578869195 } = 424945.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 424945.72 }{ 600.63 } = 1415 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 424945.72 }{ 1415 } = 600.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 424945.72 }{ 1537.2 } = 552.88 ; ;

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{ 1415**2+1537.2**2-600.63**2 }{ 2 * 1415 * 1537.2 } ) = 23° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 600.63**2+1537.2**2-1415**2 }{ 2 * 600.63 * 1537.2 } ) = 67° ; ;
 gamma = 180° - alpha - beta = 180° - 23° - 67° = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 424945.72 }{ 1776.42 } = 239.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 600.63 }{ 2 * sin 23° } = 768.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1415**2+2 * 1537.2**2 - 600.63**2 } }{ 2 } = 1446.518 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1537.2**2+2 * 600.63**2 - 1415**2 } }{ 2 } = 928.07 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1415**2+2 * 600.63**2 - 1537.2**2 } }{ 2 } = 768.599 ; ;
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