SOLUTION: Hello, I need help with this: If the hypotenuse of a right triangle is 10 units and the legs are 5 and 5 sqrt(3)units, what are the sin, cos, and tan of the smallest angle?

Algebra ->  Triangles -> SOLUTION: Hello, I need help with this: If the hypotenuse of a right triangle is 10 units and the legs are 5 and 5 sqrt(3)units, what are the sin, cos, and tan of the smallest angle?       Log On


   

Question 70641: Hello,
I need help with this: If the hypotenuse of a right triangle is 10 units and the legs are 5 and 5 sqrt(3)units, what are the sin, cos, and tan of the smallest angle?

Thank you
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I need help with this: If_the hypotenuse of a right triangle is 10 units
and the legs are 5 and 5Ö3 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 ÐA 
            / |  _
         10/  |5Ö3                side opposite ÐA      BC     5      1
          /   |        sin(ÐA) = ——————————————————— = ———— = ———— = ——— 
         /   _|                       hypotenuse        AB     10     2
       B/___|_|C                                                 _      _
           5                      side adjacent ÐA      AC     5Ö3     Ö3
                       cos(ÐA) = ——————————————————— = ———— = ————— = ————
                                      hypotenuse        AB      10      2

                                  side opposite ÐA      BC      5       1
                       tan(ÐA) = ——————————————————— = ———— = ————— = ————
                                  side adjacent ÐA      AC     5Ö3     Ö3


Your teacher may want you to rationalize the denominator of the tangent.
If so,                      _      _
                     1     Ö3     Ö3
         tan(ÐA) = ———— × ———— = ———— 
                    Ö3     Ö3      3

Edwin