Answer :
To solve the problem, we follow these steps:
1. First, convert the angle from degrees to radians. The conversion factor is
[tex]$$\theta_{\text{radians}} = \theta_{\text{degrees}} \cdot \frac{\pi}{180}.$$[/tex]
For [tex]$\theta = 35^\circ$[/tex], we have
[tex]$$\theta_{\text{radians}} = 35 \cdot \frac{\pi}{180} \approx 0.610865.$$[/tex]
2. Next, use the formula for the arc length on a circle, which is
[tex]$$s = r \theta,$$[/tex]
where [tex]$r$[/tex] is the radius of the circle and [tex]$\theta$[/tex] is the angle in radians.
3. Substitute the known values ([tex]$r = 4000$[/tex] miles and [tex]$\theta \approx 0.610865$[/tex] radians) into the formula:
[tex]$$s \approx 4000 \times 0.610865 \approx 2443.46 \text{ miles}.$$[/tex]
4. Finally, round the result to the nearest whole number, giving a distance of approximately
[tex]$$2443 \text{ miles}.$$[/tex]
Thus, the distance between the two cities A and B is approximately
[tex]$$\boxed{2443}$$[/tex] miles.
1. First, convert the angle from degrees to radians. The conversion factor is
[tex]$$\theta_{\text{radians}} = \theta_{\text{degrees}} \cdot \frac{\pi}{180}.$$[/tex]
For [tex]$\theta = 35^\circ$[/tex], we have
[tex]$$\theta_{\text{radians}} = 35 \cdot \frac{\pi}{180} \approx 0.610865.$$[/tex]
2. Next, use the formula for the arc length on a circle, which is
[tex]$$s = r \theta,$$[/tex]
where [tex]$r$[/tex] is the radius of the circle and [tex]$\theta$[/tex] is the angle in radians.
3. Substitute the known values ([tex]$r = 4000$[/tex] miles and [tex]$\theta \approx 0.610865$[/tex] radians) into the formula:
[tex]$$s \approx 4000 \times 0.610865 \approx 2443.46 \text{ miles}.$$[/tex]
4. Finally, round the result to the nearest whole number, giving a distance of approximately
[tex]$$2443 \text{ miles}.$$[/tex]
Thus, the distance between the two cities A and B is approximately
[tex]$$\boxed{2443}$$[/tex] miles.
