Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 45   b = 656   c = 657.54

Area: T = 147609.9999902
Perimeter: p = 1358.54
Semiperimeter: s = 679.27

Angle ∠ A = α = 3.92442129194° = 3°55'27″ = 0.0688490436 rad
Angle ∠ B = β = 86.07878720104° = 86°4'40″ = 1.50223422797 rad
Angle ∠ C = γ = 89.99879150702° = 89°59'53″ = 1.57107599379 rad

Height: ha = 6565.999999566
Height: hb = 454.9999999702
Height: hc = 44.89546071425

Median: ma = 656.3854929595
Median: mb = 331.0710877306
Median: mc = 328.7721633661

Inradius: r = 21.72992092838
Circumradius: R = 328.7770000218

Vertex coordinates: A[657.54; 0] B[0; 0] C[3.07880268881; 44.89546071425]
Centroid: CG[220.2066008963; 14.96548690475]
Coordinates of the circumscribed circle: U[328.77; 0.0121963575]
Coordinates of the inscribed circle: I[23.27; 21.72992092838]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.0765787081° = 176°4'33″ = 0.0688490436 rad
∠ B' = β' = 93.92221279896° = 93°55'20″ = 1.50223422797 rad
∠ C' = γ' = 90.00220849298° = 90°7″ = 1.57107599379 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 = 45+656+657.54 = 1358.54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1358.54 }{ 2 } = 679.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 679.27 * (679.27-45)(679.27-656)(679.27-657.54) } ; ; T = sqrt{ 217857599.71 } = 14760 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14760 }{ 45 } = 656 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14760 }{ 656 } = 45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14760 }{ 657.54 } = 44.89 ; ;

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{ 656**2+657.54**2-45**2 }{ 2 * 656 * 657.54 } ) = 3° 55'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45**2+657.54**2-656**2 }{ 2 * 45 * 657.54 } ) = 86° 4'40" ; ; gamma = 180° - alpha - beta = 180° - 3° 55'27" - 86° 4'40" = 89° 59'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14760 }{ 679.27 } = 21.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45 }{ 2 * sin 3° 55'27" } = 328.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 656**2+2 * 657.54**2 - 45**2 } }{ 2 } = 656.385 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 657.54**2+2 * 45**2 - 656**2 } }{ 2 } = 331.071 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 656**2+2 * 45**2 - 657.54**2 } }{ 2 } = 328.772 ; ;
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