Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.75   b = 1.32   c = 1.83

Area: T = 1.03878362106
Perimeter: p = 5.9
Semiperimeter: s = 2.95

Angle ∠ A = α = 120.7644364366° = 120°45'52″ = 2.10877357773 rad
Angle ∠ B = β = 24.35990555799° = 24°21'33″ = 0.42551457225 rad
Angle ∠ C = γ = 34.87765800543° = 34°52'36″ = 0.60987111538 rad

Height: ha = 0.75547899713
Height: hb = 1.57224791069
Height: hc = 1.13442472247

Median: ma = 0.80993361477
Median: mb = 2.24105579662
Median: mc = 1.95332600953

Inradius: r = 0.35218088849
Circumradius: R = 1.66001802433

Vertex coordinates: A[1.83; 0] B[0; 0] C[2.50551912568; 1.13442472247]
Centroid: CG[1.44550637523; 0.37880824082]
Coordinates of the circumscribed circle: U[0.915; 1.31327649489]
Coordinates of the inscribed circle: I[1.63; 0.35218088849]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 59.23656356342° = 59°14'8″ = 2.10877357773 rad
∠ B' = β' = 155.641094442° = 155°38'27″ = 0.42551457225 rad
∠ C' = γ' = 145.1233419946° = 145°7'24″ = 0.60987111538 rad

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How did we calculate this triangle?

a = 2.75 ; ; b = 1.32 ; ; c = 1.83 ; ;

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

p = a+b+c = 2.75+1.32+1.83 = 5.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.9 }{ 2 } = 2.95 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.95 * (2.95-2.75)(2.95-1.32)(2.95-1.83) } ; ; T = sqrt{ 1.08 } = 1.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.04 }{ 2.75 } = 0.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.04 }{ 1.32 } = 1.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.04 }{ 1.83 } = 1.13 ; ;

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{ 1.32**2+1.83**2-2.75**2 }{ 2 * 1.32 * 1.83 } ) = 120° 45'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.75**2+1.83**2-1.32**2 }{ 2 * 2.75 * 1.83 } ) = 24° 21'33" ; ; gamma = 180° - alpha - beta = 180° - 120° 45'52" - 24° 21'33" = 34° 52'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.04 }{ 2.95 } = 0.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.75 }{ 2 * sin 120° 45'52" } = 1.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.32**2+2 * 1.83**2 - 2.75**2 } }{ 2 } = 0.809 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.83**2+2 * 2.75**2 - 1.32**2 } }{ 2 } = 2.241 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.32**2+2 * 2.75**2 - 1.83**2 } }{ 2 } = 1.953 ; ;
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