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Topic: lame beginning trig question #2
Replies: 2   Last Post: Jun 16, 2005 12:26 AM

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 Bob Posts: 27 Registered: 1/29/05
Re: lame beginning trig question #2
Posted: Jun 16, 2005 12:23 AM

On Wed, 15 Jun 2005 23:59:09 -0400, twomble
<twomble@twiddledeedee.net> 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.

bob

Date Subject Author
6/15/05 twomble
6/16/05 Bob
6/16/05 William Elliot