A hiker makes four straight-line walks A 32 km at 140 ◦ B 27 km at 291 ◦ C 12 km at 55 ◦ D 18 km at 302

Question

How far from the starting point is the hiker after these four legs of the hike? All angles are measured in a counter-clockwise direction from the positive x-axis. Answer in units of km.

Answer 1

Here one would set down:

32cos 140° + 32 sin 140°

27cos 291° + 27sin 291°

12cos 55° + 12sin 55°

18cos 302° + 18sin 302°

Addition of the "cosine column" above is crushed by a calculator

into 1.58397645.

Addition of the "sine column" above is crushed by a calculator

into -10.0725092.

Take the hiker's final distance from the

starting point as [1.58397645² + (-10.0725092)²]^0.5.

A calculator will reduce this last to

10.19629457 (kilometers).

Here the hiker has driven himself the equivalent of

1.58397645 kilometers due East from the starting

point with a drop in position (due to the negative sign)

from there of -10.0725092 kilometers due South.

The hiker would end at the same final position if he walked

10.19629457 kilometers from the starting point in the

direction given by arctangent (-10.0725092 ÷ 1.58397645)

equal to {-81.06300622° + 360°} or 278.9369938°.

Note that 278.9369938° translates to

"8.9369938 Degrees East Of Straight South".