Find the height, h, of the triangle shown
(hint: the formula for area of a triangle is a =1/2 bh, where b is the length of the base and h is the height of the triangle.)

The first thing you should do is use the fact that the area of the triangle is:
 A = b * h * (1/2).
 From there you clear the height as a function of "c"
 Then you will have a polynomial division which you must make to find the height of the triangle.
 I attach the solution.

9514 1404 393

∠D - no∠E - noDE - yes

Step-by-step explanation:

With a single application of the Law of Cosines, you can only find one of an unknown side or an unknown angle. The other three elements in the 4-variable equation must be specified.

However, a single application of the LoC can be used to find DE. Then, knowing the three sides, either of the unknown angles can be found from an additional application of the LoC.

So, the answer is "it depends." It is yes to all if finding DE first is allowed. It is "no" to the angles if they must be found without finding DE first.