Chapter 6, Problem 12STP

(a)

To determine

To calculate:Tosketch a drawing of the situation.

Answer to Problem 12STP

Situation is drawn as follows

Explanation of Solution

Given information:A tree casts a shadow that is $32$ feet long at the same time as a stop sign casts a shadow that is $4$ feet long. The stop sign is $7$ feet tall.

Calculation:

Situation is given as a tree casts a shadow that is $32$ feet long at the same time as a stop sign casts a shadow that is $4$ feet long. The stop sign is $7$ feet tall.

Here,

$AB=$ Height of tree $=7feet$

$BC=$ Length of shadow of tree $=4feet$

$CE=$ Length of shadow of tree $=32feet$

(b)

To determine

To calculate: Tofind height of tree.

Answer to Problem 12STP

Height of tree is $56$ feet

Explanation of Solution

Given information: A tree casts a shadow that is $32$ feet long at the same time as a stop sign casts a shadow that is $4$ feet long. The stop sign is $7$ feet tall.

Calculation:

Situation is given as a tree casts a shadow that is $32$ feet long at the same time as a stop sign casts a shadow that is $4$ feet long. The stop sign is $7$ feet tall.

Here,

$AB=$ Height of tree $=7feet$

$BC=$ Length of shadow of tree $=4feet$

$CE=$ Length of shadow of tree $=32feet$

Let the height of tree be $x$

Since the shadow is casted at the same time, thus the scale factor will be same

Therefore, we have

$\frac{AB}{BC}=\frac{DE}{CE}$

On substituting the values in above proportion,

$\frac{7}{4}=\frac{x}{32}$

On solving the proportion,

$\begin{array}{l}7\times 32=x\times 4\\ x\times 4=7\times 32\\ x=\frac{7\times 32}{4}\\ x=\frac{7\times 8}{1}\\ x=56\end{array}$

Hence, tree is $56$ feet tall.