On Wed, 15 Jun 2005 23:59:09 -0400, twomble <email@example.com> wrote:
>Ok, on to Chapter 3. Exercise 54 posits "Suppose you are standing an >unknown distance away from a cliff of height H. You need to know the >height T of a tower located on top of the cliff. You know that the >angle of elevation of the bottom of the tower is B and the angle of >elevation of the top of the tower is A. Derive a formula for the >height of the tower.". > >My response is to first find the Distance to the cliff by H / Tan B. >Then T+H = D * Tan A, and (T+H)-H = T.
That is all fine. But what then is your answer? You now need to take what you did and write an expression for T in terms of H, A and B -- but not D. If you do that, you will get what you wrote below. It is algebra at this point; your trig is fine.
> >However, the answer provided is T = H(Tan A/Tan B - 1).
By the way, you mean T = H((Tan A/Tan B) - 1)
> >How do they arrive at this formula?
by doing algebra on the two trig eqns you gave. Eliminate D. Give it a try. Getting it in exactly their form takes a little looking, but is not difficult. In any case, show what form you get.