A sailboat in a lake travels 4 km due north and then 4 km due west. From there, the boat travels 5 km due north and 4 km due west. How far is the bboat from the starting point? Express your answer as a mixed radical.

Question

(How would I use radicals for this??)

Thanks!

Answer 1

Hasn't the boat effectively traveled 9 km north and 8 km west?

Don't you have a right-angled triangle with sides 8 and 9 and we have to find the hypotenuse ?

Go for it, don't go to decimals

btw, I get √145, which cannot be written as a mixed radical

Answer 2

I get �ã145 but the answer according to the answer key is 9�ã2

Answer 3

You probably wrote the question wrong,
The boat went 4km North, then 5km west
then another 4km north, then anoter 5km west

So in total it's 9km north, 9km west.
Using the Pythagorean formula
a^2 + b^2 = c^2
It'd be
81 + 81 = 162
convert 162 into a mixed radical
9√2

9√2 is the answer