Using the data statement, we plot the following diagram:
We see that the angle of the result vector is:
[tex]\theta_1=180\degree+\theta_2\text{.}[/tex]
The second angle can be computed using the trigonometric relation:
[tex]\tan \theta_2=\frac{OS}{AS}\text{.}[/tex]
Where:
• OS = opposite side to θ_2 = 780 m,
,
• AS = adjacent side to θ_2 = 360 m.
Replacing these values in the formula above, we have:
[tex]\tan \theta_2=\frac{780m}{360m}=\frac{13}{6}\Rightarrow\theta_2=\arctan (\frac{13}{6})\cong65.22\degree.[/tex]
So the resultant angle is:
[tex]\theta_1=180\degree+\theta_2\cong180\degree+65.2\degree=245.2\degree.[/tex]
Answer
The resultant angle is 245.2° to the nearest tenth.
