Question

a. what is the distance from the lighthouse to the end of the lighthouses shadow, x?
b. what is the distance from maya to the lighthouse, y?

Explanation:

Step1: Set up proportion

Since the two right - angled triangles formed by the lighthouse and the person are similar, the ratios of their corresponding sides are equal. We have the proportion $\frac{48}{6}=\frac{x}{8}$.

Step2: Solve for $x$

Cross - multiply: $6x = 48\times8$. Then $x=\frac{48\times8}{6}=64$ ft.

Step3: Find $y$

We know that $x = y + 8$, so $y=x - 8$. Substituting $x = 64$ into the equation, we get $y=64 - 8=56$ ft.

Answer:

a. 64 ft
b. 56 ft