2. A ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. This mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. When the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak?

Part I: Sketch a figure to illustrate the scenario above. Label the vertices and the lengths that are given in the question. (3 points)

Part II: Using your sketch from Part I, equation using a trigonometric ratio to find the distance a tourist will travel from the base of the mountain to its peak. Round your answer to the nearest 100th. Show your work. (2 points)

With the data given in the exercise, you can draw the right triangle shown attached, where the side BC is the height of the mountain ([tex]BC=200\ yd[/tex]), and the side AB is the distance that the tourist will travel from the base of the mountain to its peak ([tex]AB=d[/tex]).

Part II

In order to find "d", you need to use the following Trigonometric ratio:

[tex]sin\alpha =\frac{opposite}{hypotenuse}[/tex]

In this case, you can identify from the figure that:

[tex]\alpha=40\°\\\\opposite=BC=200\\\\hypotenuse=AB=d[/tex]

Substitute into [tex]sin\alpha =\frac{opposite}{hypotenuse}[/tex]:

[tex]sin(40\°)=\frac{200}{d}[/tex]

Finally, you must solve for "d" in order to find its value. This is (Rounded to the nearest 100th):

[tex]d*sin(40\°)=200\\\\d=\frac{200}{sin(40\°)}\\\\d=311.14\ yd[/tex]