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 $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 26^{\circ}$, then $\theta_{rad}=26\times\frac{\pi}{180}=\frac{13\pi}{90}$ radians.

Step2: Calculate the arc - length

The formula for the arc - length $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Here, $r = 4000$ miles and $\theta=\frac{13\pi}{90}$ radians. So $s=4000\times\frac{13\pi}{90}=\frac{5200\pi}{9}\approx\frac{5200\times 3.14159}{9}\approx1824$.

Answer:

1824