Can someone me with these two questions about right triangle trigonometry in math?

#1.  You want the height off the ground of the top of the ladder.  This height is the "opposite side" of the 60 degree angle.  The ladder length, 10 ft, is the hypotenuse.  

You want to use the sine function, which is defined as sin theta = opp / hyp.

Here, sin 60 degrees = h/(10 ft).    Since sin 60 deg = sqrt(3) / 2,

sqrt(3)        h
=     Use cross multiplication here.  2h  = (10 ft)(sqrt(3) ), or
     2        10 ft                                                         h = 5*sqrt(3)   (answer)