Question

What is the answer to this problem?

Answer 1

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.