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

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.

(How would I use radicals for this??)

Thanks!

Answer 1

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

Answer 2

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 3

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

Answer 4

To find the distance of the boat from the starting point, we can use the Pythagorean theorem. The Pythagorean theorem states that, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the two sides of the triangle represent the distance traveled north and west.

Let's break down the problem step by step:

1. Sailboat travels 4 km due north: This can be represented as moving up 4 units on a coordinate plane.

2. Sailboat then travels 4 km due west: This can be represented as moving left 4 units on the same coordinate plane.

At this point, we can visually see that the boat has traveled in a square shape, with each side measuring 4 units.

3. Sailboat travels 5 km due north: This adds 5 more units northwards.

4. Sailboat travels 4 km due west: This adds 4 more units to the left.

Now, we can see that the boat has formed a right triangle with sides measuring 4 units (horizontally) and 9 units (vertically).

To find the distance of the boat from the starting point, we use the Pythagorean theorem:

c^2 = a^2 + b^2

Where c represents the hypotenuse and a, b represent the other two sides.

In this case, a = 4 and b = 9:

c^2 = 4^2 + 9^2
c^2 = 16 + 81
c^2 = 97

Taking the square root of both sides:

c = √97

Therefore, the distance of the boat from the starting point is √97 km. This is the mixed radical form.