A man 6 ft tall casts a shadow 4 ft long , at the same time when a flag pole casts a shadow 50 ft long .The height of the flag pole is

Options

A. 80 ft
B. 75 ft
C. 60 ft
D. 70 ft

Answer

To solve the problem, we will use the concept of similar triangles. The height of the man and the length of his shadow can be compared to the height of the flagpole and its shadow since both are cast at the same time under the same conditions.

### Step-by-Step Solution:

1. **Identify the known values**:
- Height of the man (h1) = 6 ft
- Length of the man's shadow (s1) = 4 ft
- Length of the flagpole's shadow (s2) = 50 ft
- Height of the flagpole (h2) = ?

2. **Set up the proportion using similar triangles**:
Since the triangles formed by the man and his shadow and the flagpole and its shadow are similar, we can set up the following proportion:
\[ \frac{h1}{s1} = \frac{h2}{s2} \]
Substituting the known values:
\[ \frac{6}{4} = \frac{h2}{50} \]

3. **Cross-multiply to solve for h2**:
Cross-multiplying gives us:
\[ 6 \cdot 50 = 4 \cdot h2 \]
Simplifying this:
\[ 300 = 4 \cdot h2 \]

4. **Isolate h2**:
To find h2, divide both sides by 4:
\[ h2 = \frac{300}{4} \]
Calculating this gives:
\[ h2 = 75 \text{ ft} \]

5. **Conclusion**:
The height of the flagpole is 75 ft.