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July 24, 2014

July 24, 2014

Posted by **Jane** on Monday, March 29, 2010 at 9:27pm.

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

- Trig Math -
**Reiny**, Monday, March 29, 2010 at 10:51pmFrom the origin on the x-axis 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. ... (180-75)

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 x-axis or -1.225 degrees

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