Answer to Question #143950 in Physics for liam donohue

Question

A tree is subject to three forces as follows: 25 N pushing west, 10 N pushing
south (due to the slope it is growing on) and a third force of unknown magnitude and
direction (due to being tied to a stake to prevent it falling). What must the magnitude
and direction of the third force be in order that the tree experiences no net
acceleration?

Answer 1

The magnitude:

$$F=\sqrt{25^2+10^2}=27\ N$$

Direction:

$$\theta=\arctan{\frac{10}{25}}=22\degree\text{ S of W}$$