Question

Right Thangles & Pythagorean Theorem

TUIS
JAVE DOS
Two ships leave port at the same time. Ship X is heading due north and Ship Y is heading due east. Eight hours later they are 400
miles apart. If the Ship X had traveled 320 miles from the port, how many miles had Ship Y traveled?
A.
80 miles
B.
720 miles
C. 240 miles
D. 480 miles

I need help!! Can someone pls help me with this

Answer 1

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

Explanation:

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.

• Hypotenuse = 400 miles.

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

• Height = 320 miles.

To find the miles ship Y traveled in 8 hours :

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

Using Pythagorean Theorem, you can find the base :

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.