Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 45   b = 110.53   c = 99

Area: T = 2225.355547894
Perimeter: p = 254.53
Semiperimeter: s = 127.265

Angle ∠ A = α = 244.0000426611° = 24° = 0.41988797651 rad
Angle ∠ B = β = 92.51443676554° = 92°30'52″ = 1.6154680321 rad
Angle ∠ C = γ = 63.48655896835° = 63°29'8″ = 1.10880325675 rad

Height: ha = 98.90546879527
Height: hb = 40.26769950047
Height: hc = 44.95766763421

Median: ma = 102.483263487
Median: mb = 53.46875581545
Median: mc = 68.3422449839

Inradius: r = 17.48659975558
Circumradius: R = 55.31882575392

Vertex coordinates: A[99; 0] B[0; 0] C[-1.97441459596; 44.95766763421]
Centroid: CG[32.34219513468; 14.98655587807]
Coordinates of the circumscribed circle: U[49.5; 24.69553359397]
Coordinates of the inscribed circle: I[16.735; 17.48659975558]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1565.999957339° = 156° = 0.41988797651 rad
∠ B' = β' = 87.48656323446° = 87°29'8″ = 1.6154680321 rad
∠ C' = γ' = 116.5144410316° = 116°30'52″ = 1.10880325675 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 = 45+110.53+99 = 254.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 254.53 }{ 2 } = 127.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 127.27 * (127.27-45)(127.27-110.53)(127.27-99) } ; ; T = sqrt{ 4952207.01 } = 2225.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2225.36 }{ 45 } = 98.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2225.36 }{ 110.53 } = 40.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2225.36 }{ 99 } = 44.96 ; ;

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{ 110.53**2+99**2-45**2 }{ 2 * 110.53 * 99 } ) = 24° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45**2+99**2-110.53**2 }{ 2 * 45 * 99 } ) = 92° 30'52" ; ; gamma = 180° - alpha - beta = 180° - 24° - 92° 30'52" = 63° 29'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2225.36 }{ 127.27 } = 17.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45 }{ 2 * sin 24° } = 55.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 110.53**2+2 * 99**2 - 45**2 } }{ 2 } = 102.483 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 99**2+2 * 45**2 - 110.53**2 } }{ 2 } = 53.468 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 110.53**2+2 * 45**2 - 99**2 } }{ 2 } = 68.342 ; ;
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