Question

1. cain and remy live on the same straight road. from their balconies, they can see a flagpole in the distance. each person’s line of sight to the flagpole makes the same angle with the road. how do their distances from the flagpole compare?

Explanation:

Step1: Define the scenario

Let the road be a straight line, the flagpole be point $F$, Cain's position be $C$, Remy's position be $R$. Let the angle between $CF$ and the road = angle between $RF$ and the road = $\theta$. Let the perpendicular distance from $F$ to the road be $d$.

Step2: Relate distance to perpendicular

For Cain: $\sin\theta = \frac{d}{CF} \implies CF = \frac{d}{\sin\theta}$
For Remy: $\sin\theta = \frac{d}{RF} \implies RF = \frac{d}{\sin\theta}$

Step3: Compare the two distances

Since both $CF$ and $RF$ equal $\frac{d}{\sin\theta}$, they are equal.

Answer:

Cain and Remy are the same distance from the flagpole.