Answer
We should walk 385 paces at an angle of $65.4^{\circ}$ north of west.
Work Step by Step
Let $T$ be the position of the treasure from the origin:
$T = 100\hat{i}+500\hat{j}$
Let $R$ be the displacement vector along the yellow brick road:
$R = (300~sin(\theta))\hat{i}+(300~cos(\theta))\hat{j}$
$R = (300~sin(60^{\circ}))\hat{i}+(300~cos(60^{\circ}))\hat{j}$
$R = 260\hat{i}+150\hat{j}$
Let $d$ be the vector we need to walk to get to the treasure:
$R+d = T$
$d = T-R$
$d = (100\hat{i}+500\hat{j})-(260\hat{i}+150\hat{j})$
$d = -160\hat{i}+350\hat{j}$
We can find the distance we need to go:
$d = \sqrt{(-160)^2+(350)^2}$
$d = 385~paces$
We then find the angle $\theta$ north of west:
$tan(\theta) = \frac{160}{350}$
$\theta = arctan(\frac{160}{350})$
$\theta = 24.6^{\circ}$
We should walk 385 paces at an angle of $24.6^{\circ}$ north of west.
