Exercise 2 Page 69

Looking at the figure, we can see two right triangles. In both of them, the hypotenuse is unknown. We will call these missing sides $x$ and $y.$ If we add $x$ and $y,$ we will get the total distance between Sally and Jorge.

Keep in mind that these triangles are right triangles. Therefore, we can calculate these unknown distances by using the Pythagorean Theorem. Let's find $x$ and $y$ one at a time.

Finding $x$

By substituting the known values from Sally's triangle into the Pythagorean Equation, we can find the length of the hypotenuse $x.$ Note that, when solving the equation, we only considered the principal root. This is because $x$ represents a distance and therefore it must be non-negative. The hypotenuse $x$ is $1000$ yards.

Finding $y$

Similarly, by substituting the known values from Jorge's triangle into the Pythagorean Equation, we can find the length of the hypotenuse $y.$ Again, since $y$ represents a distance and therefore must be non-negative, we only kept the principal root when solving the equation. The hypotenuse $y$ is $500$ yards.

Total Distance

Finally, by adding $x$ and $y,$ we can determine the total distance between Jorge and Sally. This answer corresponds to option J.