Solve Displacement Vectors Homework

[EL ALEM]

Homework Statement

Route follewed by hiker consists of displacement vectors A, B, C. Vector A is 1550 m long in a direction 25.0 N of E. Vector B is of unknown length but in a direction of 41.0 E of S. Vector C is also of unknown length but of direction 35.0 N of W. Hiker ends up where he started (A+B+C=0). Find magnitudes of B and C.

Homework Equations

Sine law: (a/sinA)=(b/sinB)=(c/SinC)

The Attempt at a Solution

Ok so i drew the triangle and figured out all of the interior angles:
A=14.0 degrees
B=60.0 degrees
C=106.0 degrees

Also i know side a=1550 m

I used the sin law to get
(a/sinA)=(b/sinB)
(1550/sin14)=(b/sin60)
b=(1550sin60/sin14)
b=5548.6477 m

(a/sinA)=(c/sinC)
(1550/sin14)=(c/sin106)
c=(1550sin106/sin14)
c=6158.829

I was just wondering if I did this right because the numbers look pretty big to me and would like someone to double check for me.
Thanks in advance.

 

[EL ALEM]

Anyone? Id like to know if there are any errors.

 

[D H]

Those numbers are correct.

 

[EL ALEM]

Thanks a bunch

 

[rwisz]

I would first commend you for using the appropriate equations and steps to solve this problem. Your calculations seem to be correct, as the magnitudes of B and C are indeed large due to the displacement vectors being in opposite directions. However, it is always a good practice to check your work and make sure your calculations are accurate. You can do this by plugging in your calculated magnitudes for B and C into the original equation (A+B+C=0) and see if it balances out to 0. If it does, then your calculations are most likely correct. If not, then you may need to double check your calculations or consider other factors that may affect the outcome. Additionally, it may be helpful to provide units for your final answers to make them more meaningful and easier to interpret. Overall, your approach to solving this problem seems valid and I would encourage you to continue exploring and solving similar problems to strengthen your skills as a scientist.