Answer:
Step-by-step explanation:
Part b: Find the length of the sidewalk. The walk is the hypotenuse of a right 30-60-90 triangle with horizontal side 2√3. Using the 30° angle as the reference angle, we get the following from the definition of the cosine function:
cos 30° = adj / hyp, or:
√3 2√3
------- = --------
2 hyp
This simplifies to
1 2
-------- = -------
2 hyp
Cross multiplying results in: hyp = 4. The sidewalk length is 4 miles.
a. The width of the park can be found using the sine function, the now-known hypotenuse and the 30° angle:
1 opposite side
sin 30 degrees = ----- = ------------------------- or 2(opp side) = 4.
2 4
Then the opp side, which is the width of the park, is 2.
