Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 10.82   b = 10.82   c = 15.3

Area: T = 58.53661983968
Perimeter: p = 36.94
Semiperimeter: s = 18.47

Angle ∠ A = α = 45.00767048441° = 45°24″ = 0.7865515185 rad
Angle ∠ B = β = 45.00767048441° = 45°24″ = 0.7865515185 rad
Angle ∠ C = γ = 89.98765903119° = 89°59'12″ = 1.57105622836 rad

Height: ha = 10.82199997037
Height: hb = 10.82199997037
Height: hc = 7.65217906401

Median: ma = 12.0965995205
Median: mb = 12.0965995205
Median: mc = 7.65217906401

Inradius: r = 3.16992581698
Circumradius: R = 7.65500002095

Vertex coordinates: A[15.3; 0] B[0; 0] C[7.65; 7.65217906401]
Centroid: CG[7.65; 2.551059688]
Coordinates of the circumscribed circle: U[7.65; 0.00217904306]
Coordinates of the inscribed circle: I[7.65; 3.16992581698]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9933295156° = 134°59'36″ = 0.7865515185 rad
∠ B' = β' = 134.9933295156° = 134°59'36″ = 0.7865515185 rad
∠ C' = γ' = 90.01334096881° = 90°48″ = 1.57105622836 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 = 10.82+10.82+15.3 = 36.94 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36.94 }{ 2 } = 18.47 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.47 * (18.47-10.82)(18.47-10.82)(18.47-15.3) } ; ; T = sqrt{ 3426.49 } = 58.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.54 }{ 10.82 } = 10.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.54 }{ 10.82 } = 10.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.54 }{ 15.3 } = 7.65 ; ;

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{ 10.82**2+15.3**2-10.82**2 }{ 2 * 10.82 * 15.3 } ) = 45° 24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.82**2+15.3**2-10.82**2 }{ 2 * 10.82 * 15.3 } ) = 45° 24" ; ;
 gamma = 180° - alpha - beta = 180° - 45° 24" - 45° 24" = 89° 59'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.54 }{ 18.47 } = 3.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.82 }{ 2 * sin 45° 24" } = 7.65 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.82**2+2 * 15.3**2 - 10.82**2 } }{ 2 } = 12.096 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.3**2+2 * 10.82**2 - 10.82**2 } }{ 2 } = 12.096 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.82**2+2 * 10.82**2 - 15.3**2 } }{ 2 } = 7.652 ; ;
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