Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.74   b = 4   c = 2

Area: T = 2.49992491652
Perimeter: p = 8.74
Semiperimeter: s = 4.37

Angle ∠ A = α = 38.66884114611° = 38°40'6″ = 0.67548910965 rad
Angle ∠ B = β = 114.1987957057° = 114°11'53″ = 1.99331303497 rad
Angle ∠ C = γ = 27.13436314821° = 27°8'1″ = 0.47435712074 rad

Height: ha = 1.82442694637
Height: hb = 1.25496245826
Height: hc = 2.49992491652

Median: ma = 2.85501052612
Median: mb = 1.32443111417
Median: mc = 3.27992987055

Inradius: r = 0.57219105641
Circumradius: R = 2.19326585297

Vertex coordinates: A[2; 0] B[0; 0] C[-1.12331; 2.49992491652]
Centroid: CG[0.29223; 0.83330830551]
Coordinates of the circumscribed circle: U[1; 1.95113460554]
Coordinates of the inscribed circle: I[0.37; 0.57219105641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3321588539° = 141°19'54″ = 0.67548910965 rad
∠ B' = β' = 65.80220429432° = 65°48'7″ = 1.99331303497 rad
∠ C' = γ' = 152.8666368518° = 152°51'59″ = 0.47435712074 rad

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How did we calculate this triangle?

a = 2.74 ; ; b = 4 ; ; c = 2 ; ;

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

p = a+b+c = 2.74+4+2 = 8.74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.74 }{ 2 } = 4.37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.37 * (4.37-2.74)(4.37-4)(4.37-2) } ; ; T = sqrt{ 6.25 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 2.74 } = 1.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 4 } = 1.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 2 } = 2.5 ; ;

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{ 2.74**2-4**2-2**2 }{ 2 * 4 * 2 } ) = 38° 40'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-2.74**2-2**2 }{ 2 * 2.74 * 2 } ) = 114° 11'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2**2-2.74**2-4**2 }{ 2 * 4 * 2.74 } ) = 27° 8'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 4.37 } = 0.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.74 }{ 2 * sin 38° 40'6" } = 2.19 ; ;

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