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Dayton is due north of Richmond, and Easton is 16 mi due east of Richmond. Dayton is 32 mi from Easton.


How far apart are Dayton and Richmond? Round to the nearest tenth of a mile.



___ mi


Would you do 32^2-16^2 or 32^2+16^2

Verified Answer :

Edufirst

It is 32^2 - 16^2

Draw a triangle

Richmond is right above of Dayton (North). The distance between them is a side of  the right triangle. You do not know this distance , it is the unknown side.

Dayton is 16 mi to the east. It is the other side of the right triangle.

The other known length is the hypotenuse of the right triangle, which is the distance from Easton to Dayton. It is 32 mi.

As per Pythagorean theorem, (Side_1)^2 = (hypotenuse)^2 - (Side_2)^2

zbeth3e3

We need to use the Pythagorean Theorem, which states:

\(Hypotenuse^2 = (Leg_{1})^2 + (Leg_{2})^2\)

Look at the image I have attached.

Using what we know, we get:

\(32^2 = x^2 + 16^2\\\\x^2 = 32^2 - 16^2\\\\x^2 = 1024 - 256\\\\x^2 = 768\\\\\boxed{\bf{x=27.7~miles}}\)

You would have to do sqrt(32^2 - 16^2) to get the answer.

Your final answer is 27.7 miles.

Hope this helped! If you have any other questions or would like further explanation just let me know!! :)

View image zbeth3e3