Question

Josiah, Von and Ely are standing in a strawberry field. Von is 14.0 meters due west of Josiah. Ely is 36.0 meters from Von, in a direction 37.0 degrees south of east from Von's location. How far is Ely from Josiah? What is the direction of Ely's location from that of Josiah?

Answer 1

The Cosine Rule gives

$$EJ^2=VE^2+VJ^2-2\times VE\times VJ\times \cos 37^{\circ}$$

$$EJ^2=36^2+14^2-2\times 36\times 14\times \cos 37^{\circ}=687$$

$$EJ=26.2\:\rm{m}$$

The Sine Rule gives

$$\sin\theta=\frac{\sin 37^{\circ}}{26.2}\times 36=0.8269$$

$$\theta=124.2^{\circ}$$

So, the direction of Ely's location from that of Josiah is $55.8^{\circ}$ South of East.