Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.03   b = 1.28   c = 2.75

Area: T = 1.76599928977
Perimeter: p = 7.06
Semiperimeter: s = 3.53

Angle ∠ A = α = 89.83772276802° = 89°50'14″ = 1.56879554139 rad
Angle ∠ B = β = 24.98987651097° = 24°59'20″ = 0.43661362272 rad
Angle ∠ C = γ = 65.17440072102° = 65°10'26″ = 1.13875010125 rad

Height: ha = 1.16217114836
Height: hb = 2.75499889027
Height: hc = 1.28799948347

Median: ma = 1.51882967431
Median: mb = 2.8221719334
Median: mc = 1.87659064476

Inradius: r = 0.49985815574
Circumradius: R = 1.51550061136

Vertex coordinates: A[2.75; 0] B[0; 0] C[2.74663636364; 1.28799948347]
Centroid: CG[1.83221212121; 0.42766649449]
Coordinates of the circumscribed circle: U[1.375; 0.63660963169]
Coordinates of the inscribed circle: I[2.25; 0.49985815574]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.16327723198° = 90°9'46″ = 1.56879554139 rad
∠ B' = β' = 155.011123489° = 155°40″ = 0.43661362272 rad
∠ C' = γ' = 114.826599279° = 114°49'34″ = 1.13875010125 rad

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How did we calculate this triangle?

a = 3.03 ; ; b = 1.28 ; ; c = 2.75 ; ;

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

p = a+b+c = 3.03+1.28+2.75 = 7.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.06 }{ 2 } = 3.53 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.53 * (3.53-3.03)(3.53-1.28)(3.53-2.75) } ; ; T = sqrt{ 3.1 } = 1.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.76 }{ 3.03 } = 1.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.76 }{ 1.28 } = 2.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.76 }{ 2.75 } = 1.28 ; ;

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{ 3.03**2-1.28**2-2.75**2 }{ 2 * 1.28 * 2.75 } ) = 89° 50'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.28**2-3.03**2-2.75**2 }{ 2 * 3.03 * 2.75 } ) = 24° 59'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.75**2-3.03**2-1.28**2 }{ 2 * 1.28 * 3.03 } ) = 65° 10'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.76 }{ 3.53 } = 0.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.03 }{ 2 * sin 89° 50'14" } = 1.52 ; ;

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