Chapter 8.5, Problem 20PPS

a.

To determine

Find the distance of Trina and Enrique from India.

Answer to Problem 20PPS

  $119.2m$

Explanation of Solution

Given information:

Trina, Enrique and India together went to an amusement park. They went on a Ferris wheel having diameter $100m$ and on a cliff-dropping slide of $80m$ .

Calculation:

Here, we will consider the following figure:

  

Now, if $\Delta ABC$ is a right triangle with acute $\angle A$ , then the sine of $\angle A$ is the ratio of the length of the opposite $\angle A$ to the length of hypotenuse.

  $\begin{array}{l}\sin 57°=\frac{100}{x}\\ x=\frac{100}{\sin 57°}\\ x\approx 119.2\end{array}$

Hence, the distance between India and the other two is $119.2m$ .

b.

To determine

Find the length of the slide if cliff-dropping is having angle of depression $46°$ .

Answer to Problem 20PPS

  $111.2m$

Explanation of Solution

Given information:

Trina, Enrique and India together went to an amusement park. They went on a Ferris wheel having diameter $100m$ and on a cliff-dropping slide of $80m$ .

Calculation:

Here, we will consider the following figure:

  

  $\begin{array}{l}\sin 46°=\frac{80}{x}\\ x=\frac{80}{\sin 46°}\\ x\approx 111.2\end{array}$

Hence, the length of the slide is $111.2m$ .