Forces in 2D Legacy Problem #2 Guided Solution

Here we are told that Hector is applying a force upon phi dot of 67 Newtons magnitude and the direction is 30 degrees above the horizontal. This force which is at an angle to the horizontal and the vertical has two components. A component could be described as the effect of a force in a given direction. To say this 67 Newtons force has two components means that it has a portion of which is directed in the horizontal direction and a portion of which is directed in the vertical direction. We could determine these horizontal and vertical effects by simply using a sine, cosine, or tangent function of 30 degrees. So what I typically do is I draw a vector arrow that is representing the force and I draw it such that it is tilted 30 degrees above the horizontal and then I draw a horizontal line at the at the very tail of that force that stretches out horizontally and I draw it for a while and then coming down from the arrowhead of that 67 Newton force I draw another vertical line that comes down to meet that horizontal line that I draw. When I do that I have a right triangle and within that right triangle there is a 30 degree angle between the 67 Newtons and the horizontal at the tail of that 67 Newton vector. So if 67 Newtons is the hypotenuse of that right triangle I can use the sine value to determine the side opposite and I can use the cosine value to determine the side adjacent to that 30 degree angle. And so to get the horizontal side which is the side adjacent I would go 67 times the cosine of 30 degrees and to get the opposite side which is the vertical side I would go 67 times the sine of 30 degrees and that will get me my horizontal and my vertical component of that 67 Newton force.