Question

In Dania Beachthe library is 3 miles due west of the post office and the Dollar Generalis 5 miles due south of the libraryWhat is the distance the office to the Dollar General

Answer 1

the distance from the post office to Dollar General is 5.83 miles

Explanation:

Here we have

Distance from the library to the post office = 3 miles

Location of the library from the post office = 3 miles west

Location of the Dollar General from the library = 5 miles south

We note that from the description, the location the post office, the library and Dollar General form a right triangle

Therefore, the distance from the post office to Dollar General is given by the hypotenuse side of the triangle which is found as follows;

Hypotenuse² = Adjacent² + Opposite²

Substituting we get

Hypotenuse² = 3² + 5² = 34

Therefore the distance from the post office to Dollar General = √Hypotenuse

= √34 = 5.83 miles.

Answer 2

Answer: The distance is 6 miles

Step-by-step explanation: Please refer to the attached diagram for details.

The library which is point L is 3 miles due west of the post office which is point P. Also the dollar general which is point D is 5 miles south of the library.

With this bit of information we now have a right angled triangle PLD and the distance from the post office point O, to the dollar general point D which is line PD is unknown.

Having derived a right angled triangle with two sides already given, we shall apply the Pythagoras theorem which states that

AC² = AB² + BC²

Where AC is the longest side or hypotenuse and AB and BC are the other two sides. With the known values the formula can now be written as;

PD² = 5² + 3²

PD² = 25 + 9

PD² = 36

Add the square root sign to both sides of the equation

√PD² = √36

PD = 6

Therefore the distance from the post office to the dollar general is 6 miles