My answer is going to suck because I don't know how to use LaTex. I will try my best.
The first thing to do is to visualize the triangle in question. So I have an iso-triangle, with sides 10, and a base. Drawing a line from the apex to the base, we obviously see we have a right-triangle, with sides 10 (from the iso triangle), adjacent to would be side , and opposite would be (by the Pythagoreon theorom).
Now, the are of a triangle is . This is the equation that is going to help us solve all the problems.
A) We want the triangles area expressed in terms of "theta" only. However our initial equation, using is:
is the base of the ENTIRE triangle (we defined is the base of one HALF of the triangle), and
is the height of the triangle, which we defined by the Pythagorean theorem from the dimensions we had. However we have a problem. The question asks to define the equation in terms of and not . So we have to come up with a relationship between and .
by the dimentions of our triangle. Solving for
we get .
We can then plug in
everwhere we see in our original area formula to get:
Now for the rest, I will leave that to you however:
B) We are trying to figure out the rate of change, so we're probably going to be taking some derivatives here to get . We are also going to using implicit differentiation, and hopefully you can immediately spot where.
C) More derivatives, but here we are going to be looking for Maximum (and minimum if you want to test yourself) values.