Chapter 11.5, Problem 62SR

To determine

To calculate: To find how tall the building is.

Answer to Problem 62SR

Height of building is $65$ feet

Explanation of Solution

Given information: A $25$ foot flagpole casts a shadow that is $10$ feet long and a nearby building casts a shadow that is $26$ feet long

Calculation:

Given that $25$ foot flagpole casts a shadow that is $10$ feet long and a nearby building casts a shadow that is $26$ feet long

Let the height of building be $x$ feet

At a time, the ratio of height of flagpole to its shadow is equal to the height of building and its shadow.

Thus, we have

  $\frac{25}{10}=\frac{x}{26}$

On solving the above:

  $\begin{array}{l}x\times 10=25\times 26\\ x=\frac{25\times 26}{10}\\ x=\frac{5\times 13}{1}\\ x=65\end{array}$

Conclusion:

Hence, height of building is $65$ feet