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1.  For this trig equation, because we are missing angle X and we have sides AB and CB, we can use those 2 sides with sine, and figure out the angle. We know this is a sine question because we have the hypotinuse and opposite given. You begin by substituting the variables in the sine equation, then tying to isolate X. To be able to move sine to the other side of the equal sign, it would have to become negative, so it would become sin-1 multiplied by 9/4, which equals 40 degrees.

2.  For this trig equation, we have to find side CB with the knowledge of the angle of elevation and side CA. For this problem, because we are trying to find the adjacent side and we know what the hypotenuse side, we want to use an equation that has A and O in it, which is cosine. You then replace the variables in the cosine equation with the numbers given and with the unknown as X. Then, because you would end up with cos 25= X/30, to isolate X we have to do the opposite to the number under it to get rid of it and because what you do to one side you do to the other, you have to do the same to the side before the =. Because it is divided by 30, we multiply 30 by cos25 which equals X, and that is 27.2cm.

3.  For this trig equation, we need to find side AB with the knowledge of the angle of depression and side BC. Because we know what the opposite side is and we need to find the adjacent side, we will use tangent because it uses both of them. You then replace the variables with the degree and angle and put the unknown as X. Then, because you multiply the 20 you want to do the opposite to cancel it out, so you divide by 20. You then, because what we do to one side we have to do to the other, you divide 20 by tan 15, which equals X which is 74.6cm.