Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 50   b = 359.26   c = 355.77

Area: T = 8894.254992741
Perimeter: p = 765.03
Semiperimeter: s = 382.515

Angle ∠ A = α = 88.0001081196° = 8° = 0.14396282272 rad
Angle ∠ B = β = 89.99326799194° = 89°59'34″ = 1.57106685673 rad
Angle ∠ C = γ = 82.0077211961° = 82°26″ = 1.43112958591 rad

Height: ha = 355.7769997096
Height: hb = 49.51442789479
Height: hc = 509.9999995919

Median: ma = 356.6444108671
Median: mb = 179.6366325809
Median: mc = 184.7722293851

Inradius: r = 23.25220291424
Circumradius: R = 179.6330001466

Vertex coordinates: A[355.77; 0] B[0; 0] C[0.00663879754; 509.9999995919]
Centroid: CG[118.5922129325; 16.66766665306]
Coordinates of the circumscribed circle: U[177.885; 24.97772737038]
Coordinates of the inscribed circle: I[23.255; 23.25220291424]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1721.99989188° = 172° = 0.14396282272 rad
∠ B' = β' = 90.00773200806° = 90°26″ = 1.57106685673 rad
∠ C' = γ' = 97.9932788039° = 97°59'34″ = 1.43112958591 rad

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How did we calculate this triangle?

a = 50 ; ; b = 359.26 ; ; c = 355.77 ; ;

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

p = a+b+c = 50+359.26+355.77 = 765.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 765.03 }{ 2 } = 382.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 382.52 * (382.52-50)(382.52-359.26)(382.52-355.77) } ; ; T = sqrt{ 79107681.77 } = 8894.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8894.25 }{ 50 } = 355.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8894.25 }{ 359.26 } = 49.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8894.25 }{ 355.77 } = 50 ; ;

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{ 359.26**2+355.77**2-50**2 }{ 2 * 359.26 * 355.77 } ) = 8° ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+355.77**2-359.26**2 }{ 2 * 50 * 355.77 } ) = 89° 59'34" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 50**2+359.26**2-355.77**2 }{ 2 * 50 * 359.26 } ) = 82° 26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8894.25 }{ 382.52 } = 23.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 8° } = 179.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 359.26**2+2 * 355.77**2 - 50**2 } }{ 2 } = 356.644 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 355.77**2+2 * 50**2 - 359.26**2 } }{ 2 } = 179.636 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 359.26**2+2 * 50**2 - 355.77**2 } }{ 2 } = 184.772 ; ;
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