4) How tall is the palm tree?
Mariachi must know how tall is the palm tree. Fortunately, he has a mirror (to make sure he looks good, and of course, he does). He sees that the distance from his feet to the mirror is $4 \mathrm{ft}$, and that from the mirror to the palm tree is $14 \mathrm{ft}$. The height from Mariachi's toes to his eyes is $5 \mathrm{ft}$. How tall is this palm tree?
Answer
Final Answer: The height of the palm tree is \(\boxed{17.5}\) feet.
Step 1 ：Let the height of the palm tree be denoted as \(h\).
Step 2 ：Using similar triangles, we can set up the proportion: \(\frac{h}{5} = \frac{14}{4}\).
Step 3 ：Solve for \(h\) by cross-multiplying: \(h = 5 \times \frac{14}{4}\).
Step 4 ：Calculate the height of the palm tree: \(h = 5 \times 3.5 = 17.5\).
Step 5 ：Final Answer: The height of the palm tree is \(\boxed{17.5}\) feet.
