Question

Johnny is in Nebraska and needs to go to Texas, which is about 700 miles due south. From there, he will head east to Louisiana, about 400 miles from where he arrived in Texas. While he is traveling, a plane takes off from Nebraska and flies to Louisiana. Approximately how far, in miles, does the plane travel?

Answer 1

Answer: The plane travel approximately 806 miles.

Explanation:

Given: Johnny is in Nebraska and needs to go to Texas, which is about 700 miles due south. From there, he will head east to Louisiana, about 400 miles from where he arrived in Texas.

So while he is traveling, a plane takes off from Nebraska and flies to Louisiana , it will make a right triangle such that the distance he travel from Nebraska to Louisiana will become hypotenuse of the triangle.

Let H be the distance plane travel from Nebraska to Louisiana

By Pythagoras theorem, we have

`H^2=700^2+400^2\\\Rightarrow\ H^2=490000+160000\\\Rightarrow\ H^2=650000\\\Rightarrow\ H=√(650000)\\\Rightarrow\ H=806.22577483\approx806`

Hence, The plane travel approximately 806 miles.