Question

assuming earth to be a sphere of radius 4000 miles, how many miles north of the equator is city a, if it is 26° north from the equator? city a is approximately miles north of the equator. (round to the nearest whole number as needed.)

Explanation:

Step1: Convert degrees to radians

We use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Here $\theta_{deg} = 26^{\circ}$, so $\theta_{rad}=26\times\frac{\pi}{180}=\frac{13\pi}{90}$ radians.

Step2: Use arc - length formula

The arc - length formula for a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. Given $r = 4000$ miles and $\theta=\frac{13\pi}{90}$ radians. Then $s=4000\times\frac{13\pi}{90}=\frac{5200\pi}{9}\approx1815$ miles.

Answer:

1815