Calculus Question on calculating magnitude.?

Question

Find the magnitude of the resultant force and the angle (in degrees) it makes with the positive x-axis. (Give your answers correct to one decimal place.)

draw one vector from origin (0,0) in quadrant one that is 45 degrees (this is 20 lbs)

draw another vector from the origin (0,0) in quadrant four that is 30 degrees (this is 16 lbs)

Answer 1

resultant vector is v = < 20 cos 45°, 20 sin 45 ° > + < 16 cos (-30°) , 16  sin (-30°) > = < a , b >...| v | = √(a² + b²), angle of v  is arctan (b / a ).......{ about 28.7 & 12.4°}...you do the work

Answer 2

Draw what is happening on a cartesian plane. Draw the two vectors and fill in the resultant force. In the vector diagram we know one angle and the magnitude of two vectors.

The angle is 45* + 30* = 75*

Now we use the Cosine rule to find the magnitude of the resultant vector. The resultant vector is 22.1 lbs.

To find the angle it makes with the positive x-axis we can split the big triangle into two smaller ones since the x-axis intersects the big triangle. The angle where the resultant vector crosses the positive x-axis is what we are trying to find.

Use the Sin rule and the angle is 90.7* (basically 90*)