Triangles and Missing Side Lengths/ Tangents

Guest:

The end of an exit ramp from a highway is 17.5 feet above the highway. The angle of inclination of the ramp is 3 degrees. How long is the base of the ramp?

Draw the right angled triangle.
The ramp is the hypotenuse.
the height is opposite the angle.
So you have 3 degrees, the hypotenuse and the opposite side.
What trig ratio are you going to use?

Would it not be:

tan 3 = 17.5/x (opposite leg / adjacent leg)
17.5 x tan 3 = x
0.9171361374525 = x

I tried that, but the answer seems too small to be correct, unless I am doing something wrong or missing a step.

Guest:

Would it not be:

tan 3 = 17.5/x (opposite leg / adjacent leg)
17.5 x tan 3 = x
0.9171361374525 = x

I tried that, but the answer seems too small to be correct, unless I am doing something wrong or missing a step.

First, we have interpreted the question differently. I think the base of the ramp means the ramp itself. You think it means the horizontal distance. Either of us could be correct. the question is unclear.
Let us assume that your interpretation is correct.
On the computer we use * instead of x when we mean multiply. So we have

tan3 = 17.5/x
Now the 17.5 is on the TOP. If you chose to get rid of it you would have to divide. I am going to do either.

I am going to turn both sides upside down. (Because I want x on the top)
1/(tan3) = x/17.5
no multiply both sides by 17.5
1/(tan3) * 17.5 = x/17.5 * 17.5
17.5 / tan3 = x

Oh, okay. That makes a lot more sense now. Thanks for the help!