Chapter 6.5, Problem 3C

To determine

To calculate: the tallness of the nearby cactus (in feet).

Answer to Problem 3C

The nearby cactus is $26.67feet$ tall.

Explanation of Solution

Given information :

cactus tall = $5feet$

cactus shadow = $1.5feet$

nearby cactus shadow = $8feet$

Calculation : to find the how nearby cactus tall, the angle between shadow of cactus and earth are equal to the shadow of nearby cactus and earth.

Let $\theta$ be the angle so by using cactus tallness and shadow length,

  $\tan \theta =\frac{5}{1.5}$

  $\begin{array}{l}\tan \theta =\frac{tal\ln essof\text{ nearby cactus}}{8}\\ \frac{5}{1.5}=\frac{tal\ln essofnearbycactus}{8}\text{ [substitute]}\\ \frac{5}{1.5}·8=\frac{tal\ln essofnearbycactus}{8}·8\text{ [multiply 8 by both side]}\\ tal\ln essofnearbycactus=26.67feet\text{ [multiply and divide]}\end{array}$

Hence, The nearby cactus is $26.67feet$ tall.