A telephone pole casts a shadow that is 29 m long. Find the height of the telephone pole if a statue that is 38 cm tall casts a shadow 78 cm long.

To find the height of the telephone pole using the given information, we can use the concept of similar triangles. The situation involves two similar triangles: one formed by the telephone pole and its shadow, and the other formed by the statue and its shadow.

### Step 1: Set up the proportion
Since the triangles are similar, the ratio of the height to the shadow length for the telephone pole should be equal to the ratio of the height to the shadow length for the statue.

Let \( h \) be the height of the telephone pole. The proportion is:

\[
\frac{h}{29} = \frac{38}{78}
\]

### Step 2: Solve for \( h \)
Cross-multiply to solve for \( h \):

\[
h \times 78 = 38 \times 29
\]

\[
h \times 78 = 1102
\]

\[
h = \frac{1102}{78}
\]

\[
h \approx 14.13 \text{ meters}
\]

So, the height of the telephone pole is approximately **14.13 meters**.

---

Would you like more details on any of these steps, or do you have any questions?

Here are some related questions:

1. How can you use similar triangles to solve problems involving shadows and heights?
2. What other real-life situations can be modeled using similar triangles?
3. How would the solution change if the shadow lengths were measured in different units?
4. What is the significance of proportionality in similar triangles?
5. How would you check if two triangles are similar?
6. Can you apply the Pythagorean Theorem in this problem? Why or why not?
7. How can you ensure the accuracy of measurements when solving real-world problems like this?
8. What are the implications if the shadows are cast on uneven ground?

**Tip:** When dealing with similar triangles, always set up a proportion between corresponding sides to find missing lengths.

Learn how to calculate the height of a telephone pole using shadow lengths with a step-by-step solution. This problem involves similar triangles and proportionality, suitable for Grades 7-9 mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation