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Use the Pythagorean Theorem.
J
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.
By substituting the known values from Sally's triangle into the Pythagorean Equation, we can find the length of the hypotenuse x.
Substitute values
Calculate power
Add terms
Rearrange equation
sqrt(LHS)=sqrt(RHS)
Calculate root
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.
Similarly, by substituting the known values from Jorge's triangle into the Pythagorean Equation, we can find the length of the hypotenuse y.
Substitute values
Calculate power
Add terms
Rearrange equation
sqrt(LHS)=sqrt(RHS)
Calculate root
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.
Finally, by adding x and y, we can determine the total distance between Jorge and Sally. 1000+500=1500 yards This answer corresponds to option J.