Chapter 15, Problem 27CR

To determine

To Find: The height of the tower.

Answer to Problem 27CR

  $26$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Height of the Roger}=2m\\ \text{Total length of shadow of the tower and Roger}=14m\\ \text{Length of shadow of Roger alone is}=1m\end{array}$

Formula Used:

  $\text{RHS similarity rule}$

Calculation:

  

  $\begin{array}{l}\text{Height of the Roger}=2m\\ \text{Total length of shadow of the tower and Roger}=14m\\ \text{Length of shadow of Roger alone is}=1m\\ Let,\\ MN=2m\\ NO=1m\\ BC=14m\\ MN=AP=\text{Height of the Roger}\\ \text{Since, tower and Roger both are perpendicular to the surface}\text{.}\\ so,\Delta ABC~\Delta AMN\left(\text{RHS similarity rule}\right)\\ \frac{MN}{AB}=\frac{NO}{BC}\left(CPCTC\right)\\ \frac{2}{2+BP}=\frac{1}{14}\\ \text{⇒}2\times 14=2+BP\\ \text{⇒}28=2+BP\\ \text{⇒}BP=28-2\\ \text{⇒}BP=26\end{array}$

Conclusion:

Thus, the height of the tower is $26$