Chapter 9.2, Problem 28PPS

To determine

To find: The translation to the bottom of the hill.

Answer to Problem 28PPS

The coordinates of the point $B$ are $\left(x+100,y-75\right)$ .

Explanation of Solution

Given information:

The given information is:

The length of the roller coaster track from the top of a hill to the bottom of the hill is 125 feetat a 53° angle.

Calculation:

  

We note:

  $\begin{array}{l}b=AC\\ c=AB\end{array}$

We are given:

We need to determine the coordinates of the point $B$ . If $C\left(x,y\right),$ then the points $A$ and $B$ have the coordinates:

We need to determine $b,c$ . We use the sine function to determine $c$ .

  $\begin{array}{c}\sin C=\frac{c}{BC}\\ c=BC\sin C\\ c=125\sin {53}^{\circ }\end{array}$

  $\begin{array}{l}c=125.0\times 0.79863551\\ c\approx 100\end{array}$

We use the Pythagorean Theorem to determine $b$

  $\begin{array}{c}B{C}^2=A{C}^2+A{B}^2\\ {125}^2=b^2+{100}^2\\ b=75\end{array}$

The coordinates of the point $B$ are:

  $B\left(x+100,y-75\right)$

Therefore, the coordinates of the point $B$ are $\left(x+100,y-75\right)$ .