Final answer:
The magnitude of the larger force, when the angles between the resultant and two applied forces are 67° and 7° with a resultant magnitude of 990 pounds, cannot be determined without additional information.
Step-by-step explanation:
To find the magnitude of the larger force when the measures of the angles between the resultant and two applied forces are 67° and 7°, and the magnitude of the resultant is 990 pounds, we can apply the law of cosines. The law of cosines relates the sides of a triangle (in this case, the forces) to the angles between them. We will set up the equation as follows:
c^2 = a^2 + b^2 - 2ab\(cos(C))
Here, 'c' is the magnitude of the resultant force (990 pounds), 'a' and 'b' are the magnitudes of the two applied forces, and 'C' is the angle opposite of the resultant force, which is either 67° or 7°. Since we are looking for the larger force, we will use the angle of 7° as 'C' because the largest side is opposite the smallest angle in triangle geometry.
Unfortunately, without the magnitude of either force 'a' or 'b', we cannot solve this problem directly. We need additional information to determine the exact magnitude of the larger force.