Chapter 6, Problem 17CT

To determine

To calculate: the tallness of the goalpost.

Answer to Problem 17CT

The goalpost is $46.875feet$ tall.

Explanation of Solution

Given information : consider, the length of football player and shadow provided in the question,

Football player tall = $6feet$

Football player shadow = $32inches$

Football player shadow= $2.56feet$

Goal post shadow = $20feet$

Calculation : to find the how goalpost tall, the angle between shadow of football player and earth are equal to the shadow of goalpost and earth.

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

  $\tan \theta =\frac{6}{2.56}$

  $\begin{array}{l}\tan \theta =\frac{tal\ln essof\text{ goalpost}}{20}\\ \frac{6}{2.56}=\frac{tal\ln essof\text{ goalpost}}{20}\text{ [substitute]}\\ \frac{6}{2.56}·20=\frac{tal\ln essof\text{ goalpost}}{20}·20\text{ [multiply both side by 20]}\\ tal\ln essoftree=46.875feet\text{ [simplify]}\end{array}$

Hence,The goalpost is $46.875feet$ tall.