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Calculating Height in the Air

Date: 11/14/2001 at 17:16:31
From: Bobby Weidner
Subject: Math

I need to know the formula for calculating the height of an object, 
like how high in the air the object is.

Date: 11/17/2001 at 22:52:30
From: Doctor Jeremiah
Subject: Re: Math

Hi Bobby,

I learned how to do this when I was doing rockets and I wanted to know
how high they went.

What you need to know to do this is trigonometry.

      | \
      |  \
      |   \
      h    \
      |     \
      |      \
      |       \
      |        \
      |        a\
      +---d------O     -+-
                \|/     |
                 | you  | height of your eyeballs
                / \     |
      |---d------|     -+-

If you launch a rocket from the point called "launch" and you stand a 
certain distance away (labeled "d") Then if you measure the angle 
(labeled "a") bwtween you and the object you can calculate h.

Measuring the distance from you to a point directly below the object 
is easy. You can use a tape measure or you could just measure it in 

Measuring the angle is harder. To do that you need a device that you 
can build with some thread, a protractor or some cardboard, and a 
paperclip or other small weight.

If you don't have a protractor you can make one out of cardboard. Make 
a half circle of cardboard and label all the degrees from 0 in the 
middle to 90 at each edge:

 90 +---------------+   o   +---------------+ 90
    +                                       +
    +                                       +
    +                                       +
     +                                     +
     +                                     +
      +                                   +
       /                                 \
    45   +                              + 45
            +                        +
                +                +

The bigger the protractor, the more accurate your measurement of "a" 
will be.

Connect a thread to the hole in middle of the flat part so that it 
hangs down past the bottom, and put a weight on the end (I used a 
paperclip) to make it hang down.

Now stand a certain distance away from the point immediately below the 
object, look along the flat part of the protractor, and line the flat 
part up between your eye and the object. When it's lined up put your
finger on the thread to keep it from moving, and read the position in 

Now you know "a" and "d" so you can find "h" without too much trouble.

There is a function called tangent (usually abbreviated "tan" on 
calculators) that we need to use. It turns out that:

   tan(a) = h/d

So that means:

   d tan(a) = h

To do this on a calculator type in the value of "a" that you measured 
and press "tan"; then press times, enter "d," and press equals. That 
will give you "h"

But we need to add the height of your eyeballs to h to get the total 
height of the object. So the total height is:

   total height = d tan(a) + the height of your eyeballs

Is that what you were asking or did I completely misunderstand?

- Doctor Jeremiah, The Math Forum   
Associated Topics:
High School Trigonometry

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