Chapter 7.3, Problem 23PPS

To determine

To find: the height of the basket-ball goal.

Answer to Problem 23PPS

  $x=17.5ft$ .

Explanation of Solution

Given:

Alonzo is standing next to the basketball goal.

Height of the Alonzo is 5 feet 11 inch tall. And his shadow is 2 feet ball.

The basketball’s shadow is 4 feet 4 inch.

Calculation:

Assume that the heights and the shadows cast are proportional such that 2 similar triangles are formed. Now, convert each dimension in to inches then:

  $\begin{array}{l}\text{Alonzo}\text{Height}:5^{\prime }11^{″}\text{ft}=5\times 12+11=71\text{ inches}\\ \text{Alonzo}\text{shadow length}:2^{\prime }\text{ft}=2\times 12=24\text{ inches}\\ \text{Goal}\text{shadow length}:4^{\prime }{4}^{″}\text{ft}=4\times 12+4=52\text{ inches}\end{array}$

Let x be the goal heights in inches, the below figure is formed.

  

Set up the proportion:

  $\begin{array}{l}\frac{\text{Goal}\text{Height}}{\text{Alonzo}\text{Height}}=\frac{\text{Goal}\text{shadow length}}{\text{Alonzo}\text{shadow length}}\\ \frac{x}{71}=\frac{52}{24}\left\{\text{substitutes these value}\right\}\\ \Rightarrow x=\frac{52}{24}\times 71\left\{\text{cross multiplication}\right\}\\ \therefore x=\frac{923}{6}=12.8\end{array}$ .

Hence, the height of the statue is $x=12.8ft$ .