Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 5   b = 12   c = 12

Area: T = 29.34217364858
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 24.04993983611° = 24°2'58″ = 0.42197411845 rad
Angle ∠ B = β = 77.97553008194° = 77°58'31″ = 1.36109257345 rad
Angle ∠ C = γ = 77.97553008194° = 77°58'31″ = 1.36109257345 rad

Height: ha = 11.73766945943
Height: hb = 4.89902894143
Height: hc = 4.89902894143

Median: ma = 11.73766945943
Median: mb = 6.96441941386
Median: mc = 6.96441941386

Inradius: r = 2.02435680335
Circumradius: R = 6.13546062489

Vertex coordinates: A[12; 0] B[0; 0] C[1.04216666667; 4.89902894143]
Centroid: CG[4.34772222222; 1.63300964714]
Coordinates of the circumscribed circle: U[6; 1.27880429685]
Coordinates of the inscribed circle: I[2.5; 2.02435680335]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.9510601639° = 155°57'2″ = 0.42197411845 rad
∠ B' = β' = 102.0254699181° = 102°1'29″ = 1.36109257345 rad
∠ C' = γ' = 102.0254699181° = 102°1'29″ = 1.36109257345 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 = 5+12+12 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-5)(14.5-12)(14.5-12) } ; ; T = sqrt{ 860.94 } = 29.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.34 }{ 5 } = 11.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.34 }{ 12 } = 4.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.34 }{ 12 } = 4.89 ; ;

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{ 12**2+12**2-5**2 }{ 2 * 12 * 12 } ) = 24° 2'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+12**2-12**2 }{ 2 * 5 * 12 } ) = 77° 58'31" ; ; gamma = 180° - alpha - beta = 180° - 24° 2'58" - 77° 58'31" = 77° 58'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.34 }{ 14.5 } = 2.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 24° 2'58" } = 6.13 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 12**2 - 5**2 } }{ 2 } = 11.737 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 5**2 - 12**2 } }{ 2 } = 6.964 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 5**2 - 12**2 } }{ 2 } = 6.964 ; ;
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