91影视

The height of the pile $=14feet$

The base diameter of the pile $=45feet$

Therefore, the base radius of the pile$=22.5feet$

To find the angle we have the equation,

$胃={\cot }^{鈭�1}鈦�\left(\frac{r}{h}\right).......\left(1\right)$

where $r$is the radius and $h$is the height.

substituting the values of radius and height in the equation we get,

role="math" localid="1647800278814" $$\begin{gathered} 胃={\cot }^{鈭�1}鈦�\left(\frac{22.5}{14}\right) \\ \cot 鈦�胃=\frac{22.5}{14}.........\left(2\right) \end{gathered}$$

substitute $cot\left(胃\right)=\frac{1}{\tan \left(胃\right)}$in equation (2)

$$\begin{gathered} \frac{1}{\tan \left(胃\right)}=\frac{22.5}{14} \\ \begin{array}{rl}胃& ={\tan }^{鈭�1}鈦�\left(\frac{14}{22.5}\right)\\ & ={\tan }^{鈭�1}鈦�\left(0.6222\right)\\ & ={31.89}^{鈭�}\end{array} \end{gathered}$$

Therefore, the angle of repose is$31.89掳$

Here, the height is $17$feet

The angle$胃=31.89掳$

substituting this in equation 1,

localid="1647800758536" $$\begin{gathered} {31.89}^{鈭�}={\cot }^{鈭�1}鈦�\left(\frac{r}{17}\right) \\ \cot 鈦�\left({31.89}^{鈭�}\right)=\frac{r}{17}.......\left(3\right) \end{gathered}$$

substitute $cot\left(胃\right)=\frac{1}{\tan \left(胃\right)}$in equation (3)

localid="1647800948529" $$\begin{gathered} \frac{1}{\tan 鈦�\left({31.89}^{鈭�}\right)}=\frac{r}{17} \\ \tan 鈦�\left({31.89}^{鈭�}\right)=\frac{17}{r} \\ 0.6222=\frac{17}{r} \\ \begin{array}{rl}r& =\frac{17}{0.6222}\\ r& =27.32\end{array} \end{gathered}$$

Therefore the base diameter$=2脳31.89=54.64ft$

The base diameter of the pile is$122ft$

Therefore, the radius of the pile$=\frac{122}{2}=61ft$

localid="1647831822127" role="math" $$\begin{gathered} {31.89}^{鈭�}={\cot }^{鈭�1}鈦�\left(\frac{61}{h}\right) \\ \cot 鈦�{31.89}^{鈭�}=\frac{61}{h}.......\left(4\right) \end{gathered}$$

Substitute $cot\left(胃\right)=\frac{1}{\tan \left(胃\right)}$in equation (4)

role="math" localid="1647831977467" $$\begin{gathered} \tan 鈦�{31.89}^{鈭�}=\frac{h}{61} \\ 0.6222=\frac{h}{61} \\ 0.6222脳61=h \\ h=0.6222脳61 \\ h=37.95ft \end{gathered}$$

Therefore, the height of the pile is $37.95$feet.