Referring to the image below (based on vectors physics), how does he get F2X = F2Cosθ. I don't understand how he got the equation so that he knows there are equal. I circled it in orange.

Please see explanation below

Explanation:

Recall that trigonometric functions like cosine (cos) and sine (sin) of an angle are defined based on the relationships between the sides and hypotenuse of a right angle triangle:

where the terms "opposite" and "adjacent" refer to the sides opposite and adjacent to the angle in question.

Based on such, one can solve for example for the "adjacent" side (the horizontal component of the 200 N vector you need to find) to the known angle () in the following way:

answer; (arch); good luck

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards