Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is $30^{\circ},$ and from a second position 40 feet farther along this path it is $20^{\circ}.$ What is the height of the tree?

If $\mathbf{A} \cdot \mathbf{B}=0$, what is $\theta_{A B}$?

A tree trimmer wants to determine the height of a tree before cutting it down to be sure that the tree will not fall on a nearby building. It is determined that the angle of elevation to the top of the tree is $29^{\circ}$ from one point on a level path. From a point $50 \mathrm{ft}$ closer, the angle of elevation is $34^{\circ}$. Determine the height of the tree.

A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of the green. While standing on the marker and facing the green, the golfer turns $110^{\circ}$ toward his ball. He then paces off 35 yards to his ball. See the figure. How far is the ball from the center of the green?

Find the function $y=a x^{2}+b x+c$ whose graph contains the points (1,-1), (3,-1), and (-2,14).

Solve equation $32 = 5 - 3t$

Adam must fly home to St. Louis from a business meeting in Oklahoma City. One flight option flies directly to St. Louis, a distance of about 461.1 miles. A second flight option flies first to Kansas City and then connects to St. Louis. The bearing from Oklahoma City to Kansas City is $\mathrm{N} 29.6^{\circ} \mathrm{E},$ and the bearing from Oklahoma City to St. Louis is $\mathrm{N} 57.7^{\circ} \mathrm{E}$. The bearing from St. Louis to Oklahoma City is $\mathrm{S} 57.7^{\circ} \mathrm{W},$ and the bearing from St. Louis to Kansas City is $\mathrm{N} 79.4^{\circ} \mathrm{W}.$ How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight?

Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located $\mathrm{N} 55^{\circ} \mathrm{E} ;$ the call to Station Baker indicates that the ship is located $\mathrm{S} 60^{\circ} \mathrm{E}.$ If a helicopter capable of flying 200 miles per hour is dispatched from the station nearest the ship, how long will it take to reach the ship?

Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located $\mathrm{N} 55^{\circ} \mathrm{E}$; the call to Station Baker indicates that the ship is located $\mathrm{S} 60^{\circ} \mathrm{E}$. How far is each station from the ship?

A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of the green.While standing on the marker and facing the green, the golfer turns $110^{\circ}$ toward his ball. He then paces off 35 yards to his ball. How far is the ball from the center of the green?

Find the inverse function $f^{-1}$ of each function f Find the range of and the domain and range of $f^{-1}.$ $f(x)=2 \cos (3 x+2) ;-\frac{2}{3} \leq x \leq-\frac{2}{3}+\frac{\pi}{3}$

A triangular plot of land has one side along a straight road measuring 200 feet. A second side makes a $50^{\circ}$ angle with the road, and the third side makes a $43^{\circ}$ angle with the road. How long are the other two sides?

Find the work done by a force of 3 pounds acting in the direction $60^{\circ}$ to the horizontal in moving an object 6 feet from (0, 0) to (6, 0).

Beer: The following table presents the number of active breweries for samples of states located east and west of the Mississippi River.

$$\begin{array}{cc} \hline \text{East} & \text{West}\\ \hline \begin{array}{lc} \text{State} & \text{Number of Breweries}\\ \hline \text{Connecticut} & 18\\ \text{Delaware} & 10\\ \text{Florida} & 47\\ \text{Georgia} & 22\\ \text{Illinois} & 52\\ \text{Kentucky} & 13\\ \text{Maine} & 38\\ \text{Maryland} & 23\\ \text{Massachusetts} & 40\\ \text{New Hampshire} & 16\\ \text{New Jersey} & 20\\ \text{New York} & 76\\ \text{New Carolina} & 46\\ \text{Sout Carolina} & 14\\ \text{Tennessee} & 19\\ \text{Vermont} & 20\\ \end{array} & \begin{array}{lc} \text{State} & \text{Number of Breweries}\\ \hline \text{Alaska} & 17\\ \text{Arizona} & 31\\ \text{California} & 305\\ \text{Colorado} & 111\\ \text{Iowa} & 21\\ \text{Louisiana} & 6\\ \text{Minnesota} & 41\\ \text{Montana} & 30\\ \text{South Dakota} & 5\\ \text{Texas} & 37\\ \text{Utah} & 15\\ &&\\ &&\\ &&\\ &&\\ &&\\ \end{array}\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ Compute the sample standard deviation for the number of breweries east of the Mississippi River.

$\textbf{b.}\hspace{10pt}$ Compute the sample standard deviation for the number of breweries west of the Mississippi River.

$\textbf{c.}\hspace{10pt}$ Compute the range for each data set

$\textbf{d.}\hspace{10pt}$ Based on the standard deviations, which region has the greater spread in the number of breweries?

$\textbf{e.}\hspace{10pt}$ Based on the ranges, which region has the greater spread in the number of breweries?

$\textbf{f.}\hspace{10pt}$ The sample of western states happens to include California. Remove California from the sample of western states, and compute the sample standard deviation for the remaining western states. Does the result show that the standard deviation is not resistant? Explain.

$\textbf{g.}\hspace{10pt}$ Compute the range for the western states with California removed. Is the range resistant? Explain.