Hey Angel, good to see you again. Step 1: Identify the given information and the formula for distance between two points on the same latitude. The two points are P($27^\circ$N; $16^\circ$W) and Q($27^\circ$N; $97^\circ$W). The latitude ($\phi$) is $27^\circ$N. The radius of the Earth ($r$) is given as $6400 \text{ km}$. The value for $\pi$ is given as $3.142$. Since both points are on the same latitude, the distance between them along that parallel of latitude can be calculated using the formula: $$ \text{Distance} = \frac{\theta}{360^\circ} \times 2 \pi r \cos(\phi) $$ where $\theta$ is the difference in longitude. Step 2: Calculate the difference in longitude ($\theta$). Both longitudes are West, so we find the absolute difference. $$ \theta = |97^\circ \text{W} - 16^\circ \text{W}| = |97^\circ - 16^\circ| = 81^\circ $$ Step 3: Substitute the values into the distance formula and calculate. $$ \text{Distance} = \frac{81^\circ}{360^\circ} \times 2 \times 3.142 \times 6400 \text{ km} \times \cos(27^\circ) $$ First, calculate $\frac{81}{360}$: $$ \frac{81}{360} = 0.225 $$ Next, calculate $\cos(27^\circ)$: $$ \cos(27^\circ) \approx 0.8910065 $$ Now, substitute these values back into the distance formula: $$ \text{Distance} = 0.225 \times 2 \times 3.142 \times 6400 \text{ km} \times 0.8910065 $$ $$ \text{Distance} = 0.225 \times 40217.6 \text{ km} \times 0.8910065 $$ $$ \text{Distance} = 9048.96 \text{ km} \times 0.8910065 $$ $$ \text{Distance} \approx 8062.57 \text{ km} $$ The distance between the two points is approximately $8062.57 \text{ km}$. $$\boxed{\text{Distance} \approx 8062.57 \text{ km}}$$ Send me the next one 📸