Abuilding lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown. the side opposite the 30° angle measures 41 feet. a. find the length of the side of the lot opposite the 60° angle. show how you know. b. find the length of the hypotenuse of the triangular lot. show how you know.

You haven't shared the figure mentioned.  However, we can still solve this problem.

If you have a 30-60-90 triangle, then the sides opposite these angles have basic lengths 1, sqrt(3) and 2.  In other words, the side with length 2 is the hypotenuse and is opposite the right angle (90 deg).

Let's apply the Law of Sines:

  a            b              c
= =
sin A      sin B       sin C

If a = 41 ft  is opposite the 30 degre angle, then

   41 ft           x
=
sin 30        sin 60

Then x(sin 30)  = (41 ft)(sin 60), or
                 41sqrt(3)
          x = = 82sqrt(3)
                   0.5

The hypotenuse could be found using a similar approach:

   41 ft           x
=
sin 30        sin 90

In this case x will represent the length of the hypotenuse.