Question

A truck travels out of a valley up a long hill which climbs steadily at a 5 degree angle the top of. The hill is 800 vertical feet above the valley floor how many miles long is the road

Answer 1

Well, let's imagine that this is a right triangle, rather than an angle.
The verticle side is 800 and the angle of the horizontal side and the hypotenuse is 5 degrees. We can now find what we need. Since we know that one of the angles is 5 degrees and one angle is 90 degrees, we can add 90 + 5 and now we have 95. Now we do 180 - 95 = 85. This is our missing angle. Now we have a full set of angles. Now we can find the missing side lengths. Let's start with the horizontal side. Now we can find the horizontal side length with the sine rule. This gets us 9,144.042. Now we find the hypotenuse using the Pythagorean Theorem. As you may remember, a^2 + b^2 = c^2. For our purposes, we can find it by 9,144.042^2 + 800^2 = c^2. This gets us with 9,178.971. Now we can conclude that the road is 9,178.971 feet long, or 1.7384414773 miles. I hope this helps you.