Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 196   b = 264   c = 328.8

Area: T = 258721.9999921
Perimeter: p = 788.8
Semiperimeter: s = 394.4

Angle ∠ A = α = 36.59215918941° = 36°35'30″ = 0.63986437571 rad
Angle ∠ B = β = 53.41098254412° = 53°24'35″ = 0.93221773069 rad
Angle ∠ C = γ = 89.99985826647° = 89°59'55″ = 1.57107715896 rad

Height: ha = 2643.999999919
Height: hb = 1965.99999994
Height: hc = 157.3722262726

Median: ma = 281.6600284091
Median: mb = 236.3022179423
Median: mc = 164.4043892898

Inradius: r = 65.59883772619
Circumradius: R = 164.440000005

Vertex coordinates: A[328.8; 0] B[0; 0] C[116.8333090024; 157.3722262726]
Centroid: CG[148.5444363341; 52.45774209085]
Coordinates of the circumscribed circle: U[164.4; 0.00440667904]
Coordinates of the inscribed circle: I[130.4; 65.59883772619]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.4088408106° = 143°24'30″ = 0.63986437571 rad
∠ B' = β' = 126.5990174559° = 126°35'25″ = 0.93221773069 rad
∠ C' = γ' = 90.00114173353° = 90°5″ = 1.57107715896 rad

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How did we calculate this triangle?

a = 196 ; ; b = 264 ; ; c = 328.8 ; ;

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

p = a+b+c = 196+264+328.8 = 788.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 788.8 }{ 2 } = 394.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 394.4 * (394.4-196)(394.4-264)(394.4-328.8) } ; ; T = sqrt{ 669360383.59 } = 25872 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25872 }{ 196 } = 264 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25872 }{ 264 } = 196 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25872 }{ 328.8 } = 157.37 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 196**2-264**2-328.8**2 }{ 2 * 264 * 328.8 } ) = 36° 35'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 264**2-196**2-328.8**2 }{ 2 * 196 * 328.8 } ) = 53° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 328.8**2-196**2-264**2 }{ 2 * 264 * 196 } ) = 89° 59'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25872 }{ 394.4 } = 65.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 196 }{ 2 * sin 36° 35'30" } = 164.4 ; ;

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