Question 70641
<pre><font size = 3><B>I need help with this: If_the hypotenuse of a right triangle is 10 units
and the legs are 5 and 5<font face = "symbol">Ö</font>3 units, what are the sin, cos, and tan of
the smallest angle? 



              A       BC = 5 is the shortest side, so the angle it is   
             /|       opposite is the smallest angle. So we want <font face = "symbol">Ð</font>A 
            / |  _
         10/  |5<font face = "symbol">Ö</font>3                side opposite <font face = "symbol">Ð</font>A      BC     5      1
          /   |        sin(<font face = "symbol">Ð</font>A) = ——————————————————— = ———— = ———— = ——— 
         /   _|                       hypotenuse        AB     10     2
       B/___|_|C                                                 _      _
           5                      side adjacent <font face = "symbol">Ð</font>A      AC     5<font face ="symbol">Ö</font>3     <font face = "symbol">Ö</font>3
                       cos(<font face = "symbol">Ð</font>A) = ——————————————————— = ———— = ————— = ————
                                      hypotenuse        AB      10      2

                                  side opposite <font face = "symbol">Ð</font>A      BC      5       1
                       tan(<font face = "symbol">Ð</font>A) = ——————————————————— = ———— = ————— = ——<u>—</u>—
                                  side adjacent <font face = "symbol">Ð</font>A      AC     5<font face = "symbol">Ö</font>3     <font face = "symbol">Ö</font>3


Your teacher may want you to rationalize the denominator of the tangent.
If so,                      _      _
                     1     <font face = "symbol">Ö</font>3     <font face = "symbol">Ö</font>3
         tan(<font face = "symbol">Ð</font>A) = ——<u>—</u>— × ——<u>—</u>— = ———— 
                    <font face = "symbol">Ö</font>3     <font face = "symbol">Ö</font>3      3

Edwin</pre>