Vectors Statics and Forces The following forces are applied to a wall bracket: $F_1 = 100N$ at $30$ degrees above the $x$-axis, $F_2= 80N$ at $20$ degrees below the $x$-axis. Find the resultant force and its direction. I have calculated that $R= 163.36N$ and $\theta = 7.97$ degrees. But am I correct??

Hmm, let's see...

Vertical force = $100 \sin(\pi/6) - 80 \sin(\pi/9) = 22.638 \text{ N up}$

Horizontal force = $100 \cos(\pi/6) + 80 \cos(\pi/9) = 161.778 \text{ N right}$

Total force = $\sqrt{161.778^2 + 22.638^2} = 163.354 \text{ N}$

Direction = $\tan^{-1} \frac{22.638}{161.778} = 0.139 \text{ rad} = 7.966 \text{ degrees above x-axis}$

Yeah I get the same thing