3.16 4.47 3.16 triangle

Obtuse isosceles triangle.

Sides: a = 3.16   b = 4.47   c = 3.16

Area: T = 4.99327994111
Perimeter: p = 10.79
Semiperimeter: s = 5.395

Angle ∠ A = α = 44.98660857364° = 44°59'10″ = 0.78551553137 rad
Angle ∠ B = β = 90.02878285272° = 90°1'40″ = 1.57112820262 rad
Angle ∠ C = γ = 44.98660857364° = 44°59'10″ = 0.78551553137 rad

Height: ha = 3.16599996273
Height: hb = 2.23439147253
Height: hc = 3.16599996273

Median: ma = 3.53436737257
Median: mb = 2.23439147253
Median: mc = 3.53436737257

Inradius: r = 0.92554493811
Circumradius: R = 2.23550002636

Vertex coordinates: A[3.16; 0] B[0; 0] C[-0.00215348101; 3.16599996273]
Centroid: CG[1.053282173; 1.05333332091]
Coordinates of the circumscribed circle: U[1.58; 1.58107675915]
Coordinates of the inscribed circle: I[0.925; 0.92554493811]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0143914264° = 135°50″ = 0.78551553137 rad
∠ B' = β' = 89.97221714728° = 89°58'20″ = 1.57112820262 rad
∠ C' = γ' = 135.0143914264° = 135°50″ = 0.78551553137 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 = 3.16+4.47+3.16 = 10.79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.79 }{ 2 } = 5.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.4 * (5.4-3.16)(5.4-4.47)(5.4-3.16) } ; ; T = sqrt{ 24.93 } = 4.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.99 }{ 3.16 } = 3.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.99 }{ 4.47 } = 2.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.99 }{ 3.16 } = 3.16 ; ;

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{ 4.47**2+3.16**2-3.16**2 }{ 2 * 4.47 * 3.16 } ) = 44° 59'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.16**2+3.16**2-4.47**2 }{ 2 * 3.16 * 3.16 } ) = 90° 1'40" ; ;
 gamma = 180° - alpha - beta = 180° - 44° 59'10" - 90° 1'40" = 44° 59'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.99 }{ 5.4 } = 0.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.16 }{ 2 * sin 44° 59'10" } = 2.24 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 3.16**2 - 3.16**2 } }{ 2 } = 3.534 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 3.16**2 - 4.47**2 } }{ 2 } = 2.234 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 3.16**2 - 3.16**2 } }{ 2 } = 3.534 ; ;
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