Vanessa walked 100m E, 40m 20° N of E and turned 60m W. After walking another unmeasured displacement, she finds herself again in the opening of the cave where she started. What is the measurement of the unmeasured displacement?

Question

anonymous · Answer

$$\left(\begin{matrix}100 \ 0\end{matrix}\right) + \left(\begin{matrix}{40 \cos (20°)} \ {40 \sin(20°)}\end{matrix}\right) + \left(\begin{matrix} -60 \ 0\end{matrix}\right) + \left(\begin{matrix}x \ y\end{matrix}\right)= \left(\begin{matrix}0 \ 0\end{matrix}\right)$$
Solve for x and y...

anonymous · Answer

I solved it in this way. If you trace the paths, it would form a right angled triangle with the hypotenuse 100 (because she moves 60m W that is 90 degrees, so side opposite to that is hypotenuse) and the other two sides are 60+x and 40. Using pythogorous theorem you would have 100squared equals 60+x the whole square + 40 squared, solving you get x to be 31.65 which is your answer.

anonymous · Answer

e