Question

Information for the park trails is displayed at the entrance to the park office.

Answer 1

So you can use tan here, which is opposite/adjacent. (We're looking for the Adjacent)

Since we know Trail E is 1700, we're looking for the patch of trail A that is the adjacent. So if we put 42 into a tan calculator we get about 0.9.

So that means that 1,700 / adjacent = 0.9.

So we can also say

1,700/0.9 = adjacent

or, 1,700/0.9 = 1888.89

Now, we have the little patch of trail A in the smaller right triangle. We want to find the patch of trail A in the larger right triangle.

So just do 5,000 - 1,888.89

You get 3111.11

So if we know that's that, and we're looking for the hypotenuse, or Trail B, we can use cosine, because that's adjacent / hypotenuse.

So 42 in a cosine calculator is 0.74 ish.

So 3111.11 / hypotenuse = 0.74

Or 3111.11 / 0.74 = hypotenuse

Or 3111.11 / 0.74 = 4204

So Trail C should be 4204 feet long.