A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

Options

A. `21.4`m
B. `20.4`m
C. `30.4`m
D. `40.4`m

Explanation

To find the distance from the top of the flagpole to the far end of the shadow, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the components of the triangle
We have a right triangle formed by:
- The height of the flagpole (AB) = 18 m (vertical side)
- The length of the shadow (BC) = 9.6 m (horizontal side)
- The distance from the top of the pole to the end of the shadow (AC) = hypotenuse

### Step 2: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

### Step 3: Substitute the known values
Substituting the values we have:
\[ AC^2 = (18)^2 + (9.6)^2 \]

### Step 4: Calculate the squares
Calculating the squares:
- \( (18)^2 = 324 \)
- \( (9.6)^2 = 92.16 \)

### Step 5: Add the squares
Now, add the two results:
\[ AC^2 = 324 + 92.16 = 416.16 \]

### Step 6: Take the square root
To find AC, take the square root of both sides:
\[ AC = \sqrt{416.16} \]

### Step 7: Calculate the square root
Calculating the square root gives:
\[ AC \approx 20.4 \, \text{m} \]

### Conclusion
The distance from the top of the pole to the far end of the shadow is approximately **20.4 meters**.

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