Calculating the Sides of a Right Triangle

Date: 2/4/96 at 11:26:11
From: Tom
Subject: right triangles

Dear Dr.Math,

I need help on how to calculate the length of the opposite side 
of a right triangle if the length of the adjacent side and angles are 
known.  This way I will be able to determine how high my 
model rockets actually fly.

Thank you,
Tommy Welfley

Date: 6/19/96 at 10:37:26
From: Doctor Lisa
Subject: Re: right triangles

Hi Tommy!

You need to use a function called tangent to find the opposite 
side of the right triangle.  If you have a scientific or graphing 
calculator, it's the tan button.  This is how it would work.

    |\
    | \
    |  \
  x |   \
    |    \
    |     \
     ------ 25 degrees
      20 ft.

The tangent of the angle will always be the opposite side 
divided by the adjacent side of a right triangle.  In this 
case, the opposite side is x and the adjacent side is 20 feet.  
The angle measures 25 degrees.  The setup will then look like 
this:     

tan 25 = x/20     

I would like to get x by itself, so I would multiply both sides 
by 20.  This will give me 20 * tan 25 = x.  

I would now go to the calculator and get the value of tan 25.  
If you have a regular scientific calculator (a TI-30, for 
example), you would put in 25 and hit the tan button that I 
mentioned earlier.  If you have a graphing calculator (a TI-81, 
TI-82, TI-85), then you would hit the tan button first, then 
enter 25 and hit enter.  

You should get a value like 0.466307658155 (but we usually only 
use the first 4 decimal places).  Multiply this answer by 20, 
which will give you 9.3261531631, or about 9.3 feet.  
So your rocket would have gone about 9.3 feet high.

Hope this helps!

-Doctor Lisa,  The Math Forum