Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 44   b = 32   c = 15.12

Area: T = 171.2879870408
Perimeter: p = 91.12
Semiperimeter: s = 45.56

Angle ∠ A = α = 134.9277406885° = 134°55'39″ = 2.35549275013 rad
Angle ∠ B = β = 30.99114812462° = 30°59'29″ = 0.54109033878 rad
Angle ∠ C = γ = 14.08111118686° = 14°4'52″ = 0.24657617644 rad

Height: ha = 7.78554486549
Height: hb = 10.70549919005
Height: hc = 22.65660675143

Median: ma = 11.92992581496
Median: mb = 28.74655596571
Median: mc = 37.72106362619

Inradius: r = 3.75994352592
Circumradius: R = 31.07333537299

Vertex coordinates: A[15.12; 0] B[0; 0] C[37.71987301587; 22.65660675143]
Centroid: CG[17.61329100529; 7.55220225048]
Coordinates of the circumscribed circle: U[7.56; 30.14396700715]
Coordinates of the inscribed circle: I[13.56; 3.75994352592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 45.07325931149° = 45°4'21″ = 2.35549275013 rad
∠ B' = β' = 149.0098518754° = 149°31″ = 0.54109033878 rad
∠ C' = γ' = 165.9198888131° = 165°55'8″ = 0.24657617644 rad

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How did we calculate this triangle?

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

p = a+b+c = 44+32+15.12 = 91.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 91.12 }{ 2 } = 45.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.56 * (45.56-44)(45.56-32)(45.56-15.12) } ; ; T = sqrt{ 29336.79 } = 171.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.28 }{ 44 } = 7.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.28 }{ 32 } = 10.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.28 }{ 15.12 } = 22.66 ; ;

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{ 32**2+15.12**2-44**2 }{ 2 * 32 * 15.12 } ) = 134° 55'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 44**2+15.12**2-32**2 }{ 2 * 44 * 15.12 } ) = 30° 59'29" ; ;
 gamma = 180° - alpha - beta = 180° - 134° 55'39" - 30° 59'29" = 14° 4'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.28 }{ 45.56 } = 3.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 44 }{ 2 * sin 134° 55'39" } = 31.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 15.12**2 - 44**2 } }{ 2 } = 11.929 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.12**2+2 * 44**2 - 32**2 } }{ 2 } = 28.746 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 44**2 - 15.12**2 } }{ 2 } = 37.721 ; ;
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