Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 16   b = 18   c = 18

Area: T = 128.9966123973
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 52.77655999225° = 52°46'32″ = 0.92111079834 rad
Angle ∠ B = β = 63.61222000388° = 63°36'44″ = 1.11102423351 rad
Angle ∠ C = γ = 63.61222000388° = 63°36'44″ = 1.11102423351 rad

Height: ha = 16.12545154966
Height: hb = 14.33329026636
Height: hc = 14.33329026636

Median: ma = 16.12545154966
Median: mb = 14.45768322948
Median: mc = 14.45768322948

Inradius: r = 4.96113893836
Circumradius: R = 10.04768135017

Vertex coordinates: A[18; 0] B[0; 0] C[7.11111111111; 14.33329026636]
Centroid: CG[8.37703703704; 4.77876342212]
Coordinates of the circumscribed circle: U[9; 4.46552504452]
Coordinates of the inscribed circle: I[8; 4.96113893836]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.2244400078° = 127°13'28″ = 0.92111079834 rad
∠ B' = β' = 116.3887799961° = 116°23'16″ = 1.11102423351 rad
∠ C' = γ' = 116.3887799961° = 116°23'16″ = 1.11102423351 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 = 16+18+18 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-16)(26-18)(26-18) } ; ; T = sqrt{ 16640 } = 129 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 129 }{ 16 } = 16.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 129 }{ 18 } = 14.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 129 }{ 18 } = 14.33 ; ;

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{ 18**2+18**2-16**2 }{ 2 * 18 * 18 } ) = 52° 46'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+18**2-18**2 }{ 2 * 16 * 18 } ) = 63° 36'44" ; ;
 gamma = 180° - alpha - beta = 180° - 52° 46'32" - 63° 36'44" = 63° 36'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 129 }{ 26 } = 4.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 52° 46'32" } = 10.05 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 18**2 - 16**2 } }{ 2 } = 16.125 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 16**2 - 18**2 } }{ 2 } = 14.457 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 16**2 - 18**2 } }{ 2 } = 14.457 ; ;
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