Chapter 4.8, Problem 59E

To determine

To find: whether the statement is true of false.

Answer to Problem 59E

The statement is false.

Explanation of Solution

Given information:

Given statement

The leaning tower of Pisa is not vertical, but when you know the angle of elevation $\theta$ to the top of the tower as you stand $d$ feet away from it, its height $h$ can be found using the formula $h=d\tan \theta$ .

Calculation:

Let us consider the infrastructure of leaning tower of Pisa.

It is not vertical, and we can’t find the height $h$ of the tower while standing away $d$ distance from it because we don’t know the angle of elevation $\theta$ to the top of the tower as it doesn’t create a right triangle since the tower is not vertical but tilted.

This can be understood better by looking at the figure drawn below.

Therefore, the statement that the leaning tower of Pisa is not vertical and we can know its height $h$ using the formula $h=d\tan \theta$ if we know the angle of elevation $\theta$ to the top of the tower while standing $d$ feet away from it, is false.