Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 18   b = 22   c = 24

Area: T = 189.3154553059
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 45.81656148467° = 45°48'56″ = 0.87996333279 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 72.96765898339° = 72°58' = 1.27435072366 rad

Height: ha = 21.03549503399
Height: hb = 17.21104139145
Height: hc = 15.77662127549

Median: ma = 21.19896201004
Median: mb = 18.13883571472
Median: mc = 16.12545154966

Inradius: r = 5.91660797831
Circumradius: R = 12.55105406827

Vertex coordinates: A[24; 0] B[0; 0] C[8.66766666667; 15.77662127549]
Centroid: CG[10.88988888889; 5.2598737585]
Coordinates of the circumscribed circle: U[12; 3.67664210081]
Coordinates of the inscribed circle: I[10; 5.91660797831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.1844385153° = 134°11'4″ = 0.87996333279 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 107.0333410166° = 107°2' = 1.27435072366 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 = 18+22+24 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-18)(32-22)(32-24) } ; ; T = sqrt{ 35840 } = 189.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 189.31 }{ 18 } = 21.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 189.31 }{ 22 } = 17.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 189.31 }{ 24 } = 15.78 ; ;

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{ 22**2+24**2-18**2 }{ 2 * 22 * 24 } ) = 45° 48'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18**2+24**2-22**2 }{ 2 * 18 * 24 } ) = 61° 13'4" ; ;
 gamma = 180° - alpha - beta = 180° - 45° 48'56" - 61° 13'4" = 72° 58' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 189.31 }{ 32 } = 5.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 45° 48'56" } = 12.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 24**2 - 18**2 } }{ 2 } = 21.19 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 18**2 - 22**2 } }{ 2 } = 18.138 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 18**2 - 24**2 } }{ 2 } = 16.125 ; ;
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