4.595 4.595 6.5 triangle

Obtuse isosceles triangle.

Sides: a = 4.595   b = 4.595   c = 6.5

Area: T = 10.55770110738
Perimeter: p = 15.69
Semiperimeter: s = 7.845

Angle ∠ A = α = 44.98551089215° = 44°59'6″ = 0.7855138265 rad
Angle ∠ B = β = 44.98551089215° = 44°59'6″ = 0.7855138265 rad
Angle ∠ C = γ = 90.0329782157° = 90°1'47″ = 1.57113161235 rad

Height: ha = 4.59549993792
Height: hb = 4.59549993792
Height: hc = 3.24883110996

Median: ma = 5.13884342216
Median: mb = 5.13884342216
Median: mc = 3.24883110996

Inradius: r = 1.34656993083
Circumradius: R = 3.25500004391

Vertex coordinates: A[6.5; 0] B[0; 0] C[3.25; 3.24883110996]
Centroid: CG[3.25; 1.08327703665]
Coordinates of the circumscribed circle: U[3.25; -0.00216893394]
Coordinates of the inscribed circle: I[3.25; 1.34656993083]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0154891079° = 135°54″ = 0.7855138265 rad
∠ B' = β' = 135.0154891079° = 135°54″ = 0.7855138265 rad
∠ C' = γ' = 89.9770217843° = 89°58'13″ = 1.57113161235 rad

Calculate another triangle




How did we calculate this triangle?

a = 4.6 ; ; b = 4.6 ; ; c = 6.5 ; ;

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

p = a+b+c = 4.6+4.6+6.5 = 15.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.69 }{ 2 } = 7.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.85 * (7.85-4.6)(7.85-4.6)(7.85-6.5) } ; ; T = sqrt{ 111.45 } = 10.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.56 }{ 4.6 } = 4.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.56 }{ 4.6 } = 4.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.56 }{ 6.5 } = 3.25 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 4.6**2-4.6**2-6.5**2 }{ 2 * 4.6 * 6.5 } ) = 44° 59'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.6**2-4.6**2-6.5**2 }{ 2 * 4.6 * 6.5 } ) = 44° 59'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.5**2-4.6**2-4.6**2 }{ 2 * 4.6 * 4.6 } ) = 90° 1'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.56 }{ 7.85 } = 1.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.6 }{ 2 * sin 44° 59'6" } = 3.25 ; ;




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