Chapter 9.1, Problem 45E

a.

To determine

Find the height of monument from the platform.

Answer to Problem 45E

  $450.72feet$

Explanation of Solution

Given information:

the Grand View Terrace viewing platform at Mount Rushmore, $1000$ feet from the base of the monument.

  

Assume your eye level is $5.5$ feet above the platform.

Calculation:

Consider the right angle triangle, with $\theta =24°$ ,

Now calculate height $b$ ,

  $\begin{array}{l}\tan 24°=\frac{b}{1000}\\ b=\tan 24°\times 1000\\ b=455.22\\ b=455.22+eyelevel\\ b=455.22+5.5\\ b=450.72feet\end{array}$

Hence, height of monument is, $450.72feet$

b.

To determine

Find the elevation of the top of Mount Rushmore.

Answer to Problem 45E

  $5730.72feet$

Explanation of Solution

Given information:

the Grand View Terrace viewing platform at Mount Rushmore, $1000$ feet from the base of the monument.

  

The elevation of the Grand View Terrace is $5280$ feet .

Calculation:

Consider the right angle triangle, with $\theta =24°$ ,

Now calculate height $b$ ,

  $\begin{array}{l}\tan 24°=\frac{b}{1000}\\ b=\tan 24°\times 1000\\ b=455.22\\ b=455.22+eyelevel\\ b=455.22+5.5\\ b=450.72feet\end{array}$

The elevation of the top is,

  $\begin{array}{l}450.72+5280\\ =5730.72feet\end{array}$

Hence, the elevation of the top of Mount Rushmore is $5730.72feet$ .