The resultant of two forces acting on a body has a magnitude of 60 pounds. The angle between the 26 pound force and the resultant is 61 degrees. Find the magnitude of the other force to nearest tenth.

Answer 1

Forces are vectors. Add two vectors, 26+x=60

the resultant vector is the square root of the sum of one force squared plus the second force square plus 2 times the product of the two forces times the cosine of the angle between the forces, or

resultant force squared = 60²=26² + x² + 2(26x)cos(61) But you have 61 as the angle between one initial force and the resultant force? Or did you mean the angle between the two initial forces? The following uses the above formula, but that's the answer if you may have meant the angles between the two initial forces. If they are 61 degrees apart, the following is the answer. If you did mean 61 degrees between the 26 pound force and the resultant 60 pound force, the following is not the correct answer.

3600=676+x²+25.21x combine the constant terms, set all terms = 0 and use the quadratic formula to solve for x

x=42.92 pounds

check the answer

26 squared + 42.92 squared + 2(26)(42.92)cos61

=676+1842.13+2231.84(.4848)=3600.13 = about 3600 off by .13 due to rounding errors, take the square root and it's even closer to 60 pounds to two decimal places: 60.0011