Trig Math
posted by Jane on .
I need help with this problem. I don't get how to do it or how they got that answer.
A force of 50 pounds acts on an object at an angle of 45 degrees. A second force of 75 pounds acts on the object at an angle of 30 degrees. What was the direction and the magnitude of the resultant force?
The answer is F≈ 100.33 lb and Ө ≈ 1.22 degress

From the origin on the xaxis draw a line at 45 degrees with length 50
From the origin draw a line 30 degrees down into the fourth quadrant with length 75
So the angle between the two forces is 75 degrees.
Complete the parallelogram and draw the diagonal.
That diagonal is the resultant force F
I see a triangle with sides 50 and 75 and an angle of 105 degrees between them. ... (18075)
By Cosine Law
F^2 = 50^2 + 75^2  2(50)(75)cos 105
= 10066.1428
F = 100.33
Now by Sine Law
SinØ/75 = sin 105/100.33
sinØ = .72206
Ø = 46.225
so subtracting the 45 from that leaves us with Ø = 1.225 below the xaxis or 1.225 degrees