Math Workbook Question

Question

Two forces of 100 lbs and 120 lbs are acting on an object. The angle between the two forces is 50 degrees. What is the magnitude of the resultant? Round your answer to the nearest tenth if necessary.

Answer 1

100 and 120 lb at 50 degree angle

draw a parallelogram with a diagonal

angles are two 50 degree angles and two 130 degree angles

look at the triangle formed with the diagonal. it has sides 100, 120 and d

d is opposite the 130 degree angle

use the law of cosines to find d

d^2 = 100^2 + 120^2 - 2(100)(120)Cos130

=10000+14400 -23000Cos130

=24400-23000Cos130

=about 39184.11502

d = square root of that= resultant force

= about 197.949779

= about 197.9 pounds