Question

PLS HELP!!!

Answer 1

Answer: Option 4

Step-by-step explanation:

$\mathbf{u}=\langle 70 \cos 230^{\circ}, 70 \sin 230^{\circ} \rangle\\\\\mathbf{v}=\langle 60\cos 140^{\circ}, 60 \sin 140^{\circ} \rangle\\\\\mathbf{w}=\langle 80 \cos 30^{\circ}, 80 \sin 30^{\circ} \rangle\\\\\\\therefore \mathbf{u}+\mathbf{v}+\mathbf{w}=\langle 70 \cos 230^{\circ}+60 \cos 140^{\circ}+80 \cos 30^{\circ}, 70 \sin 230^{\circ}+60 \sin 140^{\circ}+80 \sin 30^{\circ} \rangle\\\\ \approx \langle -21.675, 24.944 \rangle$

$\implies |\mathbf{u}+\mathbf{v}+\mathbf{w}| \approx \sqrt{(-21.675)^2 + (24.944)^2} \approx 33.046$

Direction: The vector is in the second quadrant, so the direction is about $180^{\circ}-\arctan \left(\frac{24.944}{-21.675} \right) \approx 131^{\circ}$