Finding the resultant vector

ryant14

1. The problem statement, all variables and given/known data
In the figure below shows the path taken by a drunk skunk over a level ground, from initial point i to final point f. The angles are θ₁ = 30, θ₂ = 50, and θ₃= 80, and the distance are d₁ = 5.00 m, d₂ = 8.00 m, and d₃ = 12.0 m. What are the (a) magnitude and (b) angle of the skunk’s displacement from i to f?




2. Relevant equations
Using basic trigonometric functions, soh cah toa
Let X and Y stands for the summation of x and y.
Resultant vector = (X² + Y²)^1/2
Let * stands for the resultant vector angle, then * = tan^-1 = Y / X
3. The attempt at a solution

I have obtained the x and y component for d₁. Finding x = (5.00 m)cos30 = 4.33 m and for y, (5.00m)(sin30) = 2.5 m. However, I'm having the difficulty to find the other x and y components of d₂ and d₃ because they aren't parallel to x and y axis respectively.

For example, d₂ is diagonal and I can't simply do (8.00 m)(cos 50) to find the x component because d₂ is not parallel to x axis. Hence, connecting d₁ and d₂ will not form a right triangle which is necessary to find the x and y components using soh cah toa..

Please give me an idea how to solve this..

Thank you..

PS. If the image link above doesn't work, pls. see the copy of this question in the attached file herein..

Attached Files

Vector.doc (79.5 KB, 2 views)