Answer:
DE = about 41.843 (rounded to nearest thousandth)
EF= 34.276 (rounded)
Step-by-step explanation:
For DE, we know that the shorter side (the opposite side) is 24, while the angle across form it is 35°.  We can use trigonometry to figure this out.  SinФ equals the opposite side (in this case, 24) divided by the hypotenuse.  Set sinФ equal to a ratio of the sides like this:
sin(35) =  
 
x represents the hypotenuse length, which we don't know; 35 is the angle measure.  Next, isolate x so that the equation looks like this:
 = x
 = x 
You will need a calculator for the next part.  (and make sure you're in degree mode!).  evaluate sin(35) and divide 24 by that value.  That is DE's length.  DE = about 41.843 (rounded to nearest thousandth)
For EF, we can just use Pythagorean theorem now that we know the other sides' values.
EF^2 + 24^2 = DE^2
*a calculator might also be useful for this part.
EF= 34.276 (rounded)