Question

Part 1On the earth, 73° of latitude is how many kilometers? how many miles? (Assume that the radius of the earth is 6400 km, or 4000 mi, approximately.)On earth 73° of latitude is approximately equal to kilometers.(Type an integer or decimal rounded to one decimal place as needed.)

Answer 1

• On earth 73° of latitude is approximately equal to 8154.2 km.

,

• On earth 73° of latitude is approximately equal to 5096.4 mi.

Explanation:

The distance along a line of latitude is calculated using the formula:

`D=(\theta)/(360\degree)*2\pi R\text{ where }\begin{cases}\theta=Angle\text{ of Latitude} \\ R=Radius\text{ of the earth}\end{cases}`

Given: θ = 73°, R=6400 km

Then:

`\begin{gathered} D=(73\degree)/(360\degree)*2*\pi*6400 \\ =8154.2\text{ km} \end{gathered}`

On earth 73° of latitude is approximately equal to 8154.2 km.

When R=4000 mi.

`\begin{gathered} D=(73\degree)/(360\degree)*2*\pi*4000 \\ \approx5096.4\text{ mi.} \end{gathered}`

• On earth 73° of latitude is approximately equal to 5096.4 mi.