Find the horizontal and vertical components of each of the forces:

f) 36N acting vertically

$\displaystyle {\overrightarrow {r} } = (0, 36sin \theta)$

How do I find the $\displaystyle y$ value for the component if I cannot solve for $\displaystyle 36sin \theta$?

Find the resultant of each pair of forces acting on an object.

d) forces of 7N east and 12N north

$\displaystyle \sqrt {|{\overrightarrow {r} }|^2}$ = $\displaystyle \sqrt{7^2 + 12^2}$

$\displaystyle |{\overrightarrow {r} }| = 13.9$

$\displaystyle tan \theta = \frac {12}{7}$

$\displaystyle \theta = 60$°

Therefore, 13.9N, _____________ (How do I find the direction of this force? Can you please show me how using a diagram?)

e) forces of 6N southwest and 8N northwest

My Answer: 10N, N8°W --------- is my answer correct?

g) forces of 6N southeast and 8N northwest

My Answer: 2N, N45°W ---------------- is my answer correct?