Q2. A boy who is 1.6 m tall casts a 2.4 m shadow when he stands 8.1 m from the base of an electric light pole. How high above the ground is the light globe?

This problem involves using the properties of similar triangles. Here's the approach to solve it:

### Step 1: Understand the Setup
- The boy’s height forms a vertical line, and his shadow forms a horizontal line on the ground.
- Similarly, the light pole's height forms a vertical line, and the distance from the base of the pole to the tip of the shadow forms another horizontal line.

### Step 2: Identify Known Values
- Boy's height: 1.6 m
- Boy's shadow length: 2.4 m
- Distance from the boy to the light pole: 8.1 m

The total length of the shadow of the pole is the sum of the boy's shadow and the distance from the boy to the light pole:
\[
\text{Total shadow length} = 2.4 + 8.1 = 10.5 \text{ m}
\]

### Step 3: Set Up Proportions
Since the boy and the pole create similar triangles, the ratios of their corresponding sides (heights and shadow lengths) are equal.

Let \( h \) be the height of the light pole. The proportion is:
\[
\frac{h}{10.5} = \frac{1.6}{2.4}
\]

### Step 4: Solve for \( h \)
Now, cross-multiply and solve for \( h \):
\[
h = \frac{1.6 \times 10.5}{2.4}
\]

Let’s calculate that:

\[
h = \frac{1.6 \times 10.5}{2.4} = \frac{16.8}{2.4} = 7 \, \text{m}
\]

### Conclusion:
The height of the light globe above the ground is **7 meters**.

Would you like further details or clarifications?

Here are five related questions:
1. What is the principle of similar triangles?
2. How can shadows be used in real-world applications of geometry?
3. What happens to the shadow length when the light source is closer to the object?
4. How can you find the angle of elevation from the boy to the top of the pole?
5. How do proportions apply to solving real-life geometry problems?

**Tip:** Whenever you see a problem involving heights and shadows, think of similar triangles—they can simplify the solution!

Learn how to calculate the height of a light pole using the properties of similar triangles and proportions. A 1.6 m tall boy casts a 2.4 m shadow standing 8.1 m from the light pole. The solution involves setting up and solving a proportion equation. Suitable for students in Grades 6-8.

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