Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 180   b = 329   c = 350.91

Area: T = 29284.88657918
Perimeter: p = 859.91
Semiperimeter: s = 429.955

Angle ∠ A = α = 30.48554731368° = 30°29'8″ = 0.53220718803 rad
Angle ∠ B = β = 68.01328761859° = 68°46″ = 1.18770486232 rad
Angle ∠ C = γ = 81.50216506773° = 81°30'6″ = 1.42224721501 rad

Height: ha = 325.3887619909
Height: hb = 178.0243621835
Height: hc = 166.9088243093

Median: ma = 328.0088253021
Median: mb = 225.1865843361
Median: mc = 198.8376724412

Inradius: r = 68.11215135115
Circumradius: R = 177.4032861904

Vertex coordinates: A[350.91; 0] B[0; 0] C[67.39216789205; 166.9088243093]
Centroid: CG[139.4343892974; 55.63660810309]
Coordinates of the circumscribed circle: U[175.455; 26.21767577462]
Coordinates of the inscribed circle: I[100.955; 68.11215135115]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.5154526863° = 149°30'52″ = 0.53220718803 rad
∠ B' = β' = 111.9877123814° = 111°59'14″ = 1.18770486232 rad
∠ C' = γ' = 98.49883493227° = 98°29'54″ = 1.42224721501 rad

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How did we calculate this triangle?

a = 180 ; ; b = 329 ; ; c = 350.91 ; ;

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

p = a+b+c = 180+329+350.91 = 859.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 859.91 }{ 2 } = 429.96 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 429.96 * (429.96-180)(429.96-329)(429.96-350.91) } ; ; T = sqrt{ 857604535.84 } = 29284.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29284.89 }{ 180 } = 325.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29284.89 }{ 329 } = 178.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29284.89 }{ 350.91 } = 166.91 ; ;

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{ 329**2+350.91**2-180**2 }{ 2 * 329 * 350.91 } ) = 30° 29'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 180**2+350.91**2-329**2 }{ 2 * 180 * 350.91 } ) = 68° 46" ; ; gamma = 180° - alpha - beta = 180° - 30° 29'8" - 68° 46" = 81° 30'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29284.89 }{ 429.96 } = 68.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 180 }{ 2 * sin 30° 29'8" } = 177.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 329**2+2 * 350.91**2 - 180**2 } }{ 2 } = 328.008 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 350.91**2+2 * 180**2 - 329**2 } }{ 2 } = 225.186 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 329**2+2 * 180**2 - 350.91**2 } }{ 2 } = 198.837 ; ;
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