simple intro to physics question

[a_j]

Ok. This is a fairly simple question since it is problem #11 of Chapter 1! Yet, I cannot do it. (Hopefully this isn't a sign of things to come).

Anyway, basically the problem goes like this....

A monument rises to a height of 192m. You estimate the line of sight with the top of the arch to be 2.0 degrees above the horizontal. Apporximately how far (in km) are you from the base of the arch?

The answer is 5.5km, but I cannot get this. I can't figure out which inverse trig funtion to use. The closest I came was 6.7.

Please explain which trig function and why its that function. I tried the tangent of 2.0 and a few other methods and haven't came up with anything.

Thanks in advance,
a_j

[jamesrc]

Draw the triangle out and it should help you solve the problem. Looking from the side, the height of the triangle is 192 m (this is the distance between the ground and the top of the arch). The base of the triangle is the unknown you are trying to solve for (the distance you are away from the arch). The angle is given as 2 degrees. Tangent is a good choice to solve this problem, but how did you set it up? The tangent of the angle is equal to the ration of the opposite side to the adjacent side. So, if we call the unknown distance d:

\tan{2^\circ} = \frac{194{\rm m}}{d}

and you solve for d. (Notice you don't need to take an inverse trig function in this problem.)