VECTORS: RESULTANTS AND COMPONENTS
Figure 13 Right Triangle
As an exercise, the student should graphically find the easterly and northerly components of a
13 mile displacement at 22.6 north of east. The correct answer is 5 miles east and 12 miles
Trigonometry may also be used to determine vector components. Before explaining this method,
it may be helpful to review the fundamental trigonometric functions. Recall that trigonometry is
a branch of mathematics that deals with the relationships between angles and the length of the sides
of triangles. The relationship between an acute angle of a right triangle, shown in Figure 13, and
its sides is given by three ratios.
Before attempting to calculate vector components, first make a rough sketch that shows the
approximate location of the resultant vector in an x-y coordinate system. It is helpful to form a
visual picture before selecting the correct trigonometric function to be used. Consider the example
of Figure 12, that was used previously. This time the component vectors will be calculated.