(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A hiker starts from the trailhead and hikes 1550m in a direction 21* north of east. Then, using her compass, she hikes the second leg of her journey in a direction 41* east of south. Finally, she hikes an additional distance in the direction 18* north of west. At the end of the third leg of her trip, she is back at the trailhead where she started. What is the distance she hiked along the second leg?

2. Relevant equations

3. The attempt at a solution

Ok.. so I took this as "all of the vectors sum to 0."

Converting all angles to "actual" angles, I have 21*, 311*, and 108*, respectively.

I then figured that I could make a system of equations, one equation for each coordinate so that they sum to 0. let n be the magnitude of the second vector, and q be the magnitude of the third.

ncos(311) + qcos(108) + 1550cos(21) = 0

and

nsin(108) + qsin(311) + 1550sin(21) = 0

Valid?

I then made everything into polynomials for simplicity and got these two equations:

.95q - .75n = -555

and

-.3q + .65n = -1447.04

Which shows that q = -3684 and that n = -3926.

So, n should be the magnitude of the second vector of the trip, right? My work doesn't lead to an answer choice.

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