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Trigonometry Word Problem

Date: 06/05/2002 at 09:27:27
From: Alex
Subject: Right Triangle Trig Word Problem

As a hot-air balloon rises vertically, its angle of elevation from 
a point p on level ground 110 kilometers from the point Q directly 
underneath the ballon changes from 19 (degrees) to 38 (degrees).  
Approximately how far does the ballon rise during this period?

I am not sure how to diagram this problem. I know I should use some 
form of SOHCAHTOA, but I can not seem to set it up.


Date: 06/06/2002 at 12:52:41
From: Doctor Ian
Subject: Re: Right Triangle Trig Word problem

Hi Alex,

Here is a picture of the situation:


                     D
                     |
                     |
                     |
                     C
                     |
                     |
    A----------------B
         110 km

You're told that the angle BAC is 19 degrees.  From that, and the 
definition of sin, 

    sin(BAC) = opposite/adjacent = BC/BA

you can figure out the distance BC.  You're told that angle BAD 
is 38 degrees.  So you can use that information to figure out the 
distance BD.  

Then you just have to subtract BC from BD. 

If you're not clear on why this works, you might want to take a 
few minutes to read this:

    http://mathforum.org/library/drmath/view/53942.html 

Can you take it from here?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Trigonometry

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