Question

Add the given vectors by using the trigonometric functions and the Pythagorean theorem. Round to the nearest integer as needed

Answer 1

Let

`\begin{gathered} the\text{ vertical component of the vector be F}_y \\ the\text{ horizontal component be F}_x \end{gathered}`

Now,

`\begin{gathered} \sum_^F_y=22sin120\degree+12sin237\degree=19.05256+(-10.064046)=8.9885 \\ \sum_^F_x=22cos120\degree+12cos237\degree=-11+(-6.535668)=-17.535668 \\ \end{gathered}`

Now, the resultant force R is

`\begin{gathered} R=√(8.9885^2+(-17.535668)^2) \\ R=√(80.7931+307.49965) \\ R=√(388.29275) \\ R=19.705145 \\ R=20 \end{gathered}`

The angle theta becomes

`\begin{gathered} tan\theta=(8.9885)/(-17.535668) \\ \theta=tan^(-1)(8.9885)/(-17.535668) \\ \theta=tan^(-1)-0.512583 \\ \theta=-27.1389 \\ \theta=-27\degree \\ \theta=360-27=333\degree \end{gathered}`

Hence the answer is option C