**The ship Y traveled 240 miles which is option C).**

<u>**Step-by-step explanation:**</u>

It is instructed to use Right Triangles & Pythagorean Theorem in order to find the solution.

**So, the right angle has three sides namely, the base, the height and the hypotenuse.**

The given data are,

**Two ships leave port at the same time.**

- Ship X is heading due north ⇒ Take it as "height" of the right triangle.
- Ship Y is heading due east ⇒ Take it as "base" of the right triangle.

They were 400 miles apart after 8 hours which forms the "hypotenuse" of the right triangle.

Ship X had traveled 320 miles from the port in 8 hours. Therefore,

**<u>To find the miles ship Y traveled in 8 hours :</u>**

You can easily **find the base of triangle** which gives the number of miles traveled by ship Y in 8 hours.

**<u>Using Pythagorean Theorem, you can find the base : </u>**

**The Pythagorean triplets is (3,4,5).**

We know that, in a right triangle, **hypotenuse is the largest side** of all the three sides.

The hypotenuse is 400 miles ⇒ 5×(80) = 400

The height is 320 miles ⇒ 4×(80) = 320

**Then, the base will be 3×(80) = 240 miles.**

**Therefore, the ship Y traveled 240 miles in 8 hours.**