Question

In the diagram, HGF is a straight line. Given EF = 4 cm and HG = GF = 3 cm, find :

Answer 1

If HG and GF are both 3, then the whole length of the base is 6. The tan ratio is the side opposite the reference angle (length 4) over the side adjacent to the angle (length 6), which for us looks like this:
$tan(x)= \frac{4}{6} = \frac{2}{3}=.6666667$
Now use the inverse tan button (2nd-->tan) to get
$tan^{-1} (.66667)=33.69$
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case.  I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG.  The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
$\frac{siny}{7.211} = \frac{sin33.69}{5}$
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.