SOLUTION: Add the following vectors: A=352, Angle A=184 degrees and B=283, Angle B=348 degrees Can you please help me solve this and show me step by step how to work it? Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Add the following vectors: A=352, Angle A=184 degrees and B=283, Angle B=348 degrees Can you please help me solve this and show me step by step how to work it? Thanks!      Log On


   



Question 824359: Add the following vectors:
A=352, Angle A=184 degrees and B=283, Angle B=348 degrees
Can you please help me solve this and show me step by step how to work it? Thanks!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the x and y components
of each vector, then add x's, then
add y's. The vector sum can then be found
------------------------------------------
+A%5Bx%5D+=+-A%2Acos%284%29+
+A%5By%5D+=+-A%2Asin%284%29+
------------------------
Note that 184 degrees is in the 3rd
quadrant where both sin and cos are negative
+184+-+180+=+4+ is the angle the
vector makes with the x-axis
-----------------------------
+B%5Bx%5D+=+B%2Acos%2812%29+
+B%5By%5D+=+-B%2Asin%2812%29+
-------------------------
Vector B is in the 4th quadrant where
the cos is positive and sin is negative
+360+-+348+=+12+ is the angle B
makes with the x-axis
----------------------
+A%5Bx%5D+%2B+B%5Bx%5D+=+-A%2Acos%284%29+%2B+B%2Acos%2812%29+
+A%5Bx%5D+%2B+B%5Bx%5D+=+-352%2A.9976+%2B+283%2A.9781+
+A%5Bx%5D+%2B+B%5Bx%5D+=+-351.1552+%2B+276.8023+
+A%5Bx%5D+%2B+B%5Bx%5D+=+-74.3529+
------------------------------
+A%5By%5D+%2B+B%5By%5D+=+-A%2Asin%284%29+-+B%2Asin%2812%29+
+A%5By%5D+%2B+B%5By%5D+=+-352%2A.0698+-+283%2A.2079+
+A%5By%5D+%2B+B%5By%5D+=+-24.5696+-+58.8357+
+A%5By%5D+%2B+B%5By%5D+=+-83.4053+
------------------------------
These magnitudes both being negative means
the resultant vector is in the 3rd quadrant
Call the resultant vector +C+
+C%5E2+=+%28+-74.3529+%29%5E2+%2B+%28+-83.4053+%29%5E2+
+C%5E2+=+5528.3537+%2B+6956.4441+
+C%5E2+=+12484.7978+
+abs%28+C+%29+=+111.7354+
This is the magnitude of the resultant vector, +C+
-----------------------------
The angle, a with the x-axis is:
+cos%28a%29+=+74.3529+%2F+83.4053+
+cos%28a%29+=+.8915+
+a+=+26.9377+
This angle is in the 3rd quadrant, so I have
to add +180+ degrees
+a+%2B+180+=+26.9377+%2B+180+
+a+%2B+180+=+206.9377+
-----------------------------
So, the answer is:
111.7354 angle 206.9377
Unless I made an error ( very possible )
-----------------------------------------
This method always works. you might be asked
to do it a different way, but the result
should be the same
hope this helps