[Solved] A flagpole casts a shadow that is 49 feet long. At the same time, you who are 66 inches tall cast a shadow that is 42 inches long. How tall is the flagpole to the nearest foot? A. 55 feet B. 66 feet C. 77 feet D. 88 feet
Step 1: Understand the Concept of Similar Triangles When two triangles are similar, the ratios of the corresponding sides are equal. In this problem, the angle of the Sun’s rays creates similar triangles between you and your shadow and the flagpole and its shadow. This means:
height of flagpoleyour height=shadow of flagpoleyour shadowyour heightheight of flagpole=your shadowshadow of flagpole
Step 2: Convert All Measurements to a Common Unit To ensure consistency and ease of calculation, convert all measurements to the same unit. In this case, inches is a suitable unit.
- Your height is already given in inches: 66 inches.
- Your shadow is also in inches: 42 inches.
- The shadow of the flagpole is given in feet, so we convert it to inches: 49×12=58849×12=588 inches.
Step 3: Set Up the Proportion Using the formula for similar triangles, we can set up the proportion:
height of flagpole (h)66=5884266height of flagpole (h)=42588
Step 4: Solve for the Unknown Cross-multiplying, we get:
ℎ×42=66×588h×42=66×588
From this, we can solve for ℎh, the height of the flagpole in inches.
Step 5: Convert the Result to the Desired Unit After finding the height of the flagpole in inches, convert it back to feet for the final answer. This is done by dividing the result by 12 (since there are 12 inches in a foot).
Following these steps, we found that the flagpole is 77 feet tall.