Chapter 7.4, Problem 16WE

To determine

To Find: the height of pole shown in figure such that shadow of $2\text{ m}$ tall basketball player coincides with the shadow of pole.

Answer to Problem 16WE

  $5.5\text{ m}$

Explanation of Solution

Given:

Figure is shown as.

  

  $DE=1.6\text{ m and }DF=4.4\text{ m}$ .

Calculation:

In triangle GFD and HED.

  $\begin{array}{l}\angle DFG=\angle DEH=90\therefore \left(\text{Right angle}\right)\\ \angle D=\angle D\therefore \left(\text{Common}\right)\end{array}$

Therefore, by AA postulate $\Delta GFD\sim \Delta HED.$

Ratio of sides of two similar triangle is equal.

  $\begin{array}{l}\frac{GF}{HE}=\frac{FD}{ED}\\ \frac{GF}{2}=\frac{4.4}{1.6}\\ GF=\frac{2\times 4.4}{1.6}\\ GF=5.5\end{array}$

Therefore, the answer is $5.5\text{ m}$