Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 2   b = 22   c = 22

Area: T = 21.97772609758
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 5.21105025301° = 5°12'38″ = 0.09109404248 rad
Angle ∠ B = β = 87.39547487349° = 87°23'41″ = 1.52553261144 rad
Angle ∠ C = γ = 87.39547487349° = 87°23'41″ = 1.52553261144 rad

Height: ha = 21.97772609758
Height: hb = 1.9987932816
Height: hc = 1.9987932816

Median: ma = 21.97772609758
Median: mb = 11.09105365064
Median: mc = 11.09105365064

Inradius: r = 0.95655330859
Circumradius: R = 11.01113812757

Vertex coordinates: A[22; 0] B[0; 0] C[0.09109090909; 1.9987932816]
Centroid: CG[7.36436363636; 0.66659776053]
Coordinates of the circumscribed circle: U[11; 0.50105173307]
Coordinates of the inscribed circle: I[1; 0.95655330859]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.789949747° = 174°47'22″ = 0.09109404248 rad
∠ B' = β' = 92.60552512651° = 92°36'19″ = 1.52553261144 rad
∠ C' = γ' = 92.60552512651° = 92°36'19″ = 1.52553261144 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 = 2+22+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-2)(23-22)(23-22) } ; ; T = sqrt{ 483 } = 21.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.98 }{ 2 } = 21.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.98 }{ 22 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.98 }{ 22 } = 2 ; ;

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+22**2-2**2 }{ 2 * 22 * 22 } ) = 5° 12'38" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2**2+22**2-22**2 }{ 2 * 2 * 22 } ) = 87° 23'41" ; ; gamma = 180° - alpha - beta = 180° - 5° 12'38" - 87° 23'41" = 87° 23'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.98 }{ 23 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2 }{ 2 * sin 5° 12'38" } = 11.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 22**2 - 2**2 } }{ 2 } = 21.977 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 2**2 - 22**2 } }{ 2 } = 11.091 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 2**2 - 22**2 } }{ 2 } = 11.091 ; ;
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