We can use the fact that vectors can be resolved into components to enable us to add vectors using basic trigonometry. Consider the following example.[br][br]Albert walks 7m N 44.6[sup]o[/sup] E then 4 m E 42.2[sup]o[/sup] S. What is his displacement relative to his starting position? Use the navigation bar at the bottom of the image to click through the steps for solving this problem - see text below this image for description of steps.

[list=1][*]you should always make a scale drawing of vector problems as you work[/*][*]Draw the first vector, u[/*][*]Draw the second vector, v, head to toe[/*][*]Draw the resultant vector, r[/*][*]Resolve u into 2 right angle vectors, u[sub]y[/sub] and[/*][*]u[sub]x[/sub][/*][*]Calculate [math]u_y=u\cos\alpha[/math], [math]u_x=u\sin\alpha[/math][/*][*]Resolve v into 2 perpendicular vectors, v[sub]y[/sub] and[/*][*]v[sub]x[/sub][br][/*][*]Calculate [math]v_y=v\cos\beta[/math], [math]v_x=v_x\sin\beta[/math][br][/*][*]Calculate [math]r_x=v_x+u_y[/math][/*][*]Calculate [math]r_y=r_x+r_y[/math][/*][*]Calculate [math]r=\sqrt{r_x^2+r_y^2}[/math][/*][*]Calculate [math]\gamma=\tan^{-1}\frac{r_y}{r_x}[/math][/*][/list]In this example the answer is r = 8.2 m E16.3[sup]o[/sup] N

Rewind the frames back to the step 3. Move the blue points to create new problems. Calculate each step then advance the frame to check your answer.