In your triangle, x is a leg, 7 is a leg, and y is the hypotenuse, always the longest side. You have an angle of 45. The way that angle is related to the given side is "opposite", and if you're solving for x, the way your angle is related to the side x is "adjacent". To solve for x, you need to trig ratio that relates the side opposite to the side adjacent, which so happens to be tangent. You set up like this then:
and
which is done on your calculator in degree mode (very important!!!). x = 7, so the first choice above. In the second part, you have the same triangle but now you're solving for the length of the hypotenuse. 7 is still opposite your given angle and you're looking for hypotenuse, so the trig ratio that relates the side opposite to the hypotenuse is sin. Yours is this
and
. Using your calculator again you get that y = 9.899 or 10.