Question

The measures of the angles between the resultant and two applied forces are 26° and

20°, and the magnitude of the resultant is 80 pounds. Find the magnitude of the
larger force, to the nearest 10th of a pound.

Answer 1

48.8 lbs

Explanation:

The forces can be modeled by a triangle with acute angles 20° and 26°, and obtuse angle 134° opposite a side of length 80. The larger component force will be opposite the angle 26°, and can be found using the Law of Sines:

a/sin(A) = c/sin(C)

x/sin(26°) = 80/sin(134°)

x = 80sin(26°)/sin(134°) ≈ 48.753 . . . . pounds

The larger component force is about 48.8 pounds.