Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 44.45   b = 59.08   c = 56

Area: T = 1176.745527185
Perimeter: p = 159.53
Semiperimeter: s = 79.765

Angle ∠ A = α = 45.34549426615° = 45°20'42″ = 0.79114185486 rad
Angle ∠ B = β = 70.99333344683° = 70°59'36″ = 1.23990674334 rad
Angle ∠ C = γ = 63.66217228702° = 63°39'42″ = 1.11111066716 rad

Height: ha = 52.94769188682
Height: hb = 39.83656557835
Height: hc = 42.02766168516

Median: ma = 53.09768226451
Median: mb = 41.02879130593
Median: mc = 44.1498889567

Inradius: r = 14.75326518128
Circumradius: R = 31.24333666653

Vertex coordinates: A[56; 0] B[0; 0] C[14.476639375; 42.02766168516]
Centroid: CG[23.492213125; 14.00988722839]
Coordinates of the circumscribed circle: U[28; 13.86217445001]
Coordinates of the inscribed circle: I[20.685; 14.75326518128]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.6555057339° = 134°39'18″ = 0.79114185486 rad
∠ B' = β' = 109.0076665532° = 109°24″ = 1.23990674334 rad
∠ C' = γ' = 116.338827713° = 116°20'18″ = 1.11111066716 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 = 44.45+59.08+56 = 159.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 159.53 }{ 2 } = 79.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 79.77 * (79.77-44.45)(79.77-59.08)(79.77-56) } ; ; T = sqrt{ 1384729.43 } = 1176.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1176.75 }{ 44.45 } = 52.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1176.75 }{ 59.08 } = 39.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1176.75 }{ 56 } = 42.03 ; ;

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{ 59.08**2+56**2-44.45**2 }{ 2 * 59.08 * 56 } ) = 45° 20'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 44.45**2+56**2-59.08**2 }{ 2 * 44.45 * 56 } ) = 70° 59'36" ; ; gamma = 180° - alpha - beta = 180° - 45° 20'42" - 70° 59'36" = 63° 39'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1176.75 }{ 79.77 } = 14.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 44.45 }{ 2 * sin 45° 20'42" } = 31.24 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 59.08**2+2 * 56**2 - 44.45**2 } }{ 2 } = 53.097 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 56**2+2 * 44.45**2 - 59.08**2 } }{ 2 } = 41.028 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 59.08**2+2 * 44.45**2 - 56**2 } }{ 2 } = 44.149 ; ;
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