Question

given the concentric circles with center c and with angle c=75°

Answer 1

Arc Length of circle with radius CA = 35π/6 yard = 18.3 yard

Arc Length of circle with radius CN = 35π/3 yard = 36.7 yard

Arc Length of circle with radius CT = 35π/2 yard = 55.0 yard

Arc Length of circle with radius CO = 70π/3 yard = 73.3 yard

Step-by-step explanation:

The given angle = 75° = $75^\circ\times\frac{\pi}{180^\circ}$ radian

                                     = $\frac{5\pi}{12}$ radian

We know that

$\text{Angle}=\frac{\text{Arc}}{\text{Radius}}$

or, $\text{Arc}=\text{Angle}\times\text{Radius}$

Where, Angle is in radian

Thus,

Arc Length of circle with radius CA

$=\frac{5\pi}{12}\times CA$

$=\frac{5\pi}{12}\times 14$

$=\frac{35\pi}{6}$ yard

$=5.83\pi$ yard

$=18.3$ yard

Arc Length of circle with radius CN

$=\frac{5\pi}{12}\times CN$

$=\frac{5\pi}{12}\times (14+14)$

$=\frac{35\pi}{3}$ yard

$=11.67\pi$ yard

$=36.7$ yard

Arc Length of circle with radius CT

$=\frac{5\pi}{12}\times CT$

$=\frac{5\pi}{12}\times (14+14+14)$

$=\frac{35\pi}{2}$ yard

$=17.5\pi$ yard

$=55.0$ yard

Arc Length of circle with radius CO

$=\frac{5\pi}{12}\times CO$

$=\frac{5\pi}{12}\times (14+14+14+14)$

$=\frac{70\pi}{3}$ yard

$=23.33\pi$ yard

$=73.3$ yard

Hope this answer is helpful.

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