Can someone help me solve for this expression?

The law for this particular one would be:
#a/sin(90)=h/sinC#
Now the sin of 90 is 1, so therefore:
#a=h/sinC#
#SinC*a=h#
The answer you have picked should be correct

We can try all the answers out.

We can simplify all the answers and find the right one by using #"SOH CAH TOA"#:

#sin="opposite"/"hypotenuse"#

#cos="adjacent"/"hypotenuse"#

#tan="opposite"/"adjacent"#

The first option is #csinB#. Since #angle B# isn't a part of the right triangle, we can't actually compute it in terms of the lengths in question, so this answer is probably wrong.

The next option is #asinC#. #sinC# is the opposite side of #C# divided by the hypotenuse of that triangle. That would be #h/a#. Multiplying this value by #a# gets #a*h/a# or just #h#. Since this is what the question was asking for, that's the right answer. Let's check the rest anyway:

The third option is #bsinC#. We know from before that #sinC# is #h/a#. Multiplying this by #b# gets #b*h/a#, which can't be simplified. This isn't the height of the triangle, so this isn't the right answer.

The last option is #asinB#. We know from before that we can't actually compute #sinB#, so this answer is also wrong.

That means the correct answer #asinC#.