A vertical stick 15 cm long casts it shodow 10 cm long on the gound. At the same time a flag pole casts a shadow 60 cm long. Find the height of the flag pole :

Options

A. 40 cm
B. 45 cm
C. 90 cm
D. none of these

Answer

To solve the problem of finding the height of the flagpole based on the given information about the vertical stick and its shadow, we can use the concept of similar triangles. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Identify the given information:**
- Height of the vertical stick (let's call it \( h_1 \)) = 15 cm
- Length of the shadow of the vertical stick (let's call it \( s_1 \)) = 10 cm
- Length of the shadow of the flagpole (let's call it \( s_2 \)) = 60 cm
- Height of the flagpole (let's call it \( h_2 \)) = ?

2. **Set up the proportion using similar triangles:**
Since the sun's rays create similar triangles for both the stick and the flagpole, we can set up the following proportion:
\[ \frac{h_1}{s_1} = \frac{h_2}{s_2} \]
Substituting the known values:
\[ \frac{15 \text{ cm}}{10 \text{ cm}} = \frac{h_2}{60 \text{ cm}} \]

3. **Cross-multiply to solve for \( h_2 \):**
\[ 15 \text{ cm} \times 60 \text{ cm} = 10 \text{ cm} \times h_2 \]
\[ 900 = 10h_2 \]

4. **Isolate \( h_2 \):**
\[ h_2 = \frac{900}{10} = 90 \text{ cm} \]

5. **Conclusion:**
The height of the flagpole is \( 90 \text{ cm} \).