To solve this problem, we use the principle of similar triangles since the ruler and the pole create proportionate triangles.

Step 1: Extract the given data

• Height of ruler: 1 foot (12 inches).
• Shadow of ruler: 8 inches.
• Shadow of pole: 18 feet 7 inches, which is equivalent to $18 \times 12 + 7 = 223$ inches.
• Let the height of the pole be $h$ (in inches).

Step 2: Set up the proportion

The ratio of the height to the shadow is the same for both objects: $\frac{\text{Height of ruler}}{\text{Shadow of ruler}} = \frac{\text{Height of pole}}{\text{Shadow of pole}}$ $\frac{12}{8} = \frac{h}{223}$

Step 3: Solve for $h$

Cross-multiply: $h = \frac{12 \cdot 223}{8}$ $h = 334.5 \, \text{inches}.$

Step 4: Convert to feet and inches

$334.5 \, \text{inches} = 27 \, \text{feet} \, 10.5 \, \text{inches}.$

Final Answer:

The height of the pole is 27 feet 10.5 inches.

Would you like a breakdown of the steps?

Related Questions:

1. What would happen if the ruler was not held perpendicular?
2. How do we handle units in mixed measurements like this problem?
3. Could we use this method for objects with curved shadows?
4. How does the length of the shadow depend on the angle of the sun?
5. How can we apply this principle to calculate the height of a tree?

Tip: Always ensure units are consistent before solving proportions!