2.5 4.167 4.167 triangle

Acute isosceles triangle.

Sides: a = 2.5   b = 4.1676666666   c = 4.1676666666

Area: T = 4.96884333398
Perimeter: p = 10.8333333332
Semiperimeter: s = 5.4176666666

Angle ∠ A = α = 34.91552062532° = 34°54'55″ = 0.60993853081 rad
Angle ∠ B = β = 72.54223968734° = 72°32'33″ = 1.26661036727 rad
Angle ∠ C = γ = 72.54223968734° = 72°32'33″ = 1.26661036727 rad

Height: ha = 3.97547466719
Height: hb = 2.38548480035
Height: hc = 2.38548480035

Median: ma = 3.97547466719
Median: mb = 2.73222660515
Median: mc = 2.73222660515

Inradius: r = 0.91772492321
Circumradius: R = 2.18439267429

Vertex coordinates: A[4.1676666666; 0] B[0; 0] C[0.75500000001; 2.38548480035]
Centroid: CG[1.63988888887; 0.79549493345]
Coordinates of the circumscribed circle: U[2.0833333333; 0.6555178023]
Coordinates of the inscribed circle: I[1.25; 0.91772492321]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0854793747° = 145°5'5″ = 0.60993853081 rad
∠ B' = β' = 107.4587603127° = 107°27'27″ = 1.26661036727 rad
∠ C' = γ' = 107.4587603127° = 107°27'27″ = 1.26661036727 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 2.5 ; ; b = 4.17 ; ; c = 4.17 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 2.5+4.17+4.17 = 10.83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.83 }{ 2 } = 5.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.42 * (5.42-2.5)(5.42-4.17)(5.42-4.17) } ; ; T = sqrt{ 24.69 } = 4.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.97 }{ 2.5 } = 3.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.97 }{ 4.17 } = 2.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.97 }{ 4.17 } = 2.38 ; ;

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{ 4.17**2+4.17**2-2.5**2 }{ 2 * 4.17 * 4.17 } ) = 34° 54'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.5**2+4.17**2-4.17**2 }{ 2 * 2.5 * 4.17 } ) = 72° 32'33" ; ; gamma = 180° - alpha - beta = 180° - 34° 54'55" - 72° 32'33" = 72° 32'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.97 }{ 5.42 } = 0.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.5 }{ 2 * sin 34° 54'55" } = 2.18 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.17**2+2 * 4.17**2 - 2.5**2 } }{ 2 } = 3.975 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.17**2+2 * 2.5**2 - 4.17**2 } }{ 2 } = 2.732 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.17**2+2 * 2.5**2 - 4.17**2 } }{ 2 } = 2.732 ; ;
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