E Question Hel 7392 Two forces of 5 and 9 pounds act at an a

E Question Hel 7.3.92 Two forces of 5 and 9 pounds act at an angle of 43 to each other Find the resultant force and the angle of the resultant force to each of the two forces. The magnitude of the resultant force is approximately lb (Do not round until the final answer Then round to the nearest hundredth as needed.)

Solution

In order to calculate the required magnitude it is necessary to use the cosine rule

R = sqrt( 5^2 + 9^2 - 2*5*9cos43)

= 6.34 lb

R makes with the positive x-axis, the sine rule is used:

sin(theta)/9 = sin137/R

sintheta = 9*sin137/6.34 = 0.968

theta = 75.50 deg (resultant force makes angle with +ve x axis)