The lion first runs 200 yards at 20 deg. south of west, then 300 yards at 40 deg. west of north, and finally 400 yards at 10 deg east of north at which point it catches up to the deer. How far from the starting point, and in what direction is the point where the lion and the deer meet?

Question

The lion first runs 200 yards at 20 deg. south of west, then 300 yards at 40 deg. west of north, and finally 400 yards at 10 deg east of north at which point it catches up to the deer.  How far from the starting point, and in what direction is the point where the lion and the deer meet?

Henry · Answer

D = 200yds[200o] + 300yds[130o] + 400yds
[80o].

X = 200*Cos200 + 300*cos130o + 400*Cos80
= -311.3 Yds.

Y = 200*sin200 + 300*sin130 + 400*sin80 = 555.3 Yds.

Tan Ar = Y/X = 555.3/-311.3 = -1.78391
Ar = -60.73o = Reference angle.
A = -60.73 + 180 = 119o CCW = 29o W. of N. = Direction.

D = Y/sin A = 555.3/sin119 = 635 Yds. @
29o W. of N.