Question

You found a treasure map and it said: à ƒ ƒ ¢ € œ Start at the well, go 100m straight south, then 30m 40 degrees north of west, then 25m straight east and finally 45m 75 degrees south of east.à ƒ ƒ ¢ €  How far from the well and in what direction is the hidden treasure? Use graphical method. Verify your answer in component method.

Answer 1

According to graphical method, the distance from the well is 120 m at 85° S of E.

Apply the component method:

$$A_E=0,\\ A_S=100,\\ B_E=-30\cos40°=-22.98,\\ B_S=-30\sin40°=-19.28,\\ C_E=25,\\ C_S=0,\\ D_E=45\cos75°=11.65,\\ D_S=45\sin75°=43.47.\\\space\\ R_E=A_E+B_E+C_E+D_E=13.67,\\ R_S=124.2,\\\space\\ R=\sqrt{R_E^2+R_S^2}=122\text{ m},\\\space\\ \theta=\tan^{-1}\frac{R_S}{R_E}=83.72°.$$